Preparation

• Position a rack in the center of the oven, and heat the oven to 225°F. Line an 18-by-13-inch baking sheet (if you don’t have a sheet that large, line 2 smaller sheets) with parchment paper. Draw three 10-by-3-inch rectangles at least 3 inches apart on one side of the parchment paper, then turn the parchment over and liberally coat the other side of the paper with nonstick cooking spray or butter.

  In a food processor, pulse the 1/2 cup hazelnuts until ground to a fine powder. (Stop grinding once they are powdery; if you continue, they will become a paste.) Transfer to a medium bowl. Repeat with the 1/2 cup almonds, and add the ground almonds to the hazelnuts. Sift the confectioners’ sugar into the bowl holding the ground nuts. Add the salt and stir with a rubber spatula until all of the ingredients are well mixed.

  Using a stand mixer fitted with the whip attachment (or a handheld mixer), beat the egg whites on medium speed for 3 to 4 minutes, or until they hold soft peaks. (This will take 6 to 7 minutes with a handheld mixer.) The whites will start to froth and turn into bubbles, and eventually the yellowy viscous part will disappear. Keep whipping until you can see the tines of your whip leaving a slight trail in the whites. To test for the soft-peak stage, stop the mixer and lift the whip out of the whites; the whites should peak and then droop.

  On medium speed, add the granulated sugar in three equal additions, mixing for 30 seconds after each addition. When all of the granulated sugar has been incorporated, increase the speed to high and beat for about 15 seconds longer. The meringue should be slightly glossy and white and somewhat stiff. Scrape the meringue into a large bowl.

  Sprinkle the nut-sugar mixture on top of the meringue. Working quickly and gently, use a rubber spatula to fold the nuts into the meringue, scraping the sides of the bowl to catch any loose nuts. The final consistency will be soupy, gloupy, and puddingy.

  Fit a pastry bag with a 1/2-inch round plain tip and fill the bag with the meringue. Following the guidelines you drew on the underside of the parchment paper, pipe 3 rectangles of meringue, “fill in” the rectangles to form your individual layers. Space the rectangles about 3 inches apart (they will expand in the oven).

  Bake for about 3 hours, or until thedacquoiserectangles are firm to the touch. Turn off the oven and leave the rectangles in the closed oven for at least 6 hours or for up to 12 hours.

To make the chocolate ganache

• Place the chocolate in a medium heatproof bowl. In a small saucepan, scald the cream over medium-high heat (bubbles start to form around the edge of the pan, but the cream is not boiling). Pour the hot cream over the chocolate and let sit for about 1 minute, then slowly whisk the chocolate and cream together until the chocolate is completely melted and the mixture is smooth. You should have about 4 cups. Let cool, cover, and store at room temperature for up to overnight. (The ganache can be made up to 1 week in advance and stored in an airtight container in the refrigerator. Remove it from the refrigerator 1 day before using.)

To make the buttercream

• In a small saucepan, stir together the granulated sugar and water. Place the pan over high heat, bring to a boil, and cook, without stirring, for 3 to 4 minutes, or until the syrup registers 238°F on a candy thermometer (the soft-ball stage). Meanwhile, fit the stand mixer with the whip attachment (or use a handheld mixer) and beat together the eggs and egg yolk on medium speed for 3 to 4 minutes, or until pale and light.

  When the syrup is ready, remove from the heat. On low speed, slowly add the syrup into the eggs, drizzling it down the side of the bowl to keep it from hitting the whip and spattering. Turn the speed up to medium and whip for 6 to 8 minutes, or until the mixture turns light and fluffy, is pale, and is cool to the touch. Turn the speed down to low and add the butter, a few chunks as a time. Increase the speed to medium and continue to whip for 4 to 5 minutes. The mixture will break and look curdled at first, but don’t worry. It will soon become smooth and silky.

  Add the espresso powder and salt and whip until completely combined. You should have about 3 cups. Use within 30 minutes, or cover and leave at room temperature for up to 8 hours, and then beat vigorously with a wood spoon until smooth before using. (Or, transfer to an airtight container and store in the refrigerator for up to 5 days, then bring to room temperature and beat with the stand mixer fitted with the paddle attachment for a few minutes until smooth before using.)

To assemble the cake

• When thedacquoiserectangles are ready, carefully peel them from the parchment paper. Using a small paring knife or a small, serrated knife, trim the edges so they are even and the rectangles are all about the same size. The rectangles are fairly delicate at this point, and if you are not careful, they could shatter. The best way to avoid this is to shave off a little piece at a time until the rectangles are roughly uniform. If a rectangle shatters as you are trimming it, don’t fret. That rectangle can be the middle layer. If 2 or all 3 rectangles shatter, again don’t fret. You can piece them together as you assemble the cake. The cake will not be quite as neat, but the final product will taste the same.

  Cut a piece of cardboard the size of the dacquoise rectangles and place one rectangle on the cardboard. Fit a pastry bag fitted with the 1/2-inch round plain tip and fill with about half of the ganache. Pipe a layer of ganache about 1/2 inch thick on top of thedacquoise. Gently press a seconddacquoiserectangle directly on top of the ganache layer and press lightly to adhere thedacquoiseto the ganache. Fill the pastry bag with about two-thirds of the espresso buttercream and pipe a layer of buttercream about 1/2 inch thick on top of the seconddacquoiselayer.

  Top the buttercream with the lastdacquoiserectangle, placing it upside down so the flat side is on top. Press lightly to adhere this last rectangle to the buttercream. Use a small offset spatula to spread the remaining buttercream into the gaps between the layers and to spread a very thin layer all over thedacquoise. Do your best to make the exterior of the cake as smooth as you can—you will need to use a fair amount of buttercream to fill in all the gaps.

  Place the cake in the refrigerator for at least 1 hour to chill all of the layers. (At this point, the cake can be well wrapped in plastic wrap and stored in the refrigerator for up to 2 days or in the freezer for up to 2 weeks. If frozen, thaw overnight in the refrigerator before serving.)

  When ready to serve, spoon the remaining ganache into a small heatproof bowl, place over (not touching) simmering water in a saucepan, and heat just until melted. (Or, place in a microwave-safe bowl and microwave on low power for 30 to 45 seconds, or just until melted and warmed enough to pour freely—not warmer than that). Place a wire rack on a baking sheet (to catch the drips), and place the cake on the rack. Pour the melted ganache evenly over the entire dacquoise, so it covers the top and drips down the sides. Use a small offset spatula to level off the ganache on the top of the cake. Then, with the spatula, spread the ganache that drips down the sides so that it covers the sides evenly. Some of the ganache may mix into the buttercream, which is okay, because the sides will be covered with sliced almonds. Now, press the sliced almonds into the sides of the cake, covering them completely. (It helps to tilt the cake with one hand and press the almonds with your other hand.) Place the cake on a cake plate, and press the whole hazelnuts along the top edge for decoration.

  The cake can be stored in an airtight container in the refrigerator for up to 2 days.