Preparation

Make the pastry cream:

• In a medium saucepan, warm the milk over medium heat (if you’re using a vanilla bean, add it now) just until a skin forms. Take the pan off the heat. In a medium mixing bowl, combine the sugar, flour, and salt. Add the yolks, beating with a wooden spoon. Whisk in the warm milk in a thin stream, whisking constantly. Return the milk mixture to the saucepan. Cook over medium heat, whisking constantly, until the mixture is extremely thick and gluey (you’ll need to switch to a wooden spoon), about 5 minutes. If you’re using vanilla extract, stir it in now. Immediately force the pastry cream through a sieve. Gently press a sheet of waxed paper or plastic onto the surface of the hot pastry cream to prevent a skin from forming. Let cool and then refrigerate until ready to use it.

• Line a heavy baking sheet (or an insulated sheet or two sheets sandwiched together) with parchment or butter it. Roll the dough into a rectangle about 13×16 inches and about 1/8 inch thick. Stir the chilled pastry cream to soften it and then spread it over the dough in a thin layer. Scatter the chocolate chips evenly over the surface. Roll the rectangle into a cylinder from the wider side and pinch the long edge to seal. Put the cylinder on the baking sheet. Cut the cylinder in half lengthwise, splitting it into two thin strips. Arrange the strips parallel to one another so that the filling is facing up, push them together, and wrap them around each other to form a twist, working from the center.
  

• Position a rack in the middle on the oven and heat the oven to 350°F. Cover the shaped dough and proof until it’s large, puffy, and remains indented when lightly pressed with your fingertip, about 45 minutes.
• Brush the braid with the beaten egg, taking care not to smear the filling or dislodge the chocolate bits. Bake until golden brown, about 35 minutes, rotating the pan halfway through baking. Let cool on a rack for 1 hour before slicing.

Make Ahead Tips

The dough can be made up to four days ahead of time and refrigerated, covered.