Preparation

Make the blueberries

• In a small saucepan, combine the sugar, thyme, and 2 Tbs. water. Cook over low heat, stirring, until the sugar dissolves. Add the blueberries, lemon zest, and salt. Raise the heat to medium high and bring the mixture to a boil. Cook, stirring occasionally, until the syrup thickens slightly and the berries are warm but most are still whole, 1 to 2 minutes. Remove from the heat.

Make the cake

• Position a rack in the center of the oven and heat the oven to 325°F. Butter and flour a 9×5-inch loaf pan.
• In a small bowl, whisk together the flour, polenta, thyme, and salt.
• In a stand mixer fitted with the paddle attachment or in a large bowl using an electric hand mixer, beat the softened butter and sugar on medium-high speed until fluffy, about 2 minutes. Add the eggs one at a time, mixing well after each addition. Add the lemon juice and vanilla and mix briefly to combine. Reduce the speed to low and add the flour gradually until just combined.
• Scrape the batter into the prepared pan and smooth the top, then tap the pan on the counter to pop any large air bubbles. Bake until a tester inserted in the center comes out with just a few small, moist crumbs attached, 1-1/4 to 1-1/2 hours. (If the top starts to get too dark, lay a piece of foil loosely over the cake.) Cool in the pan on a rack for 30 minutes, then invert onto a serving plate or cutting board. Slice and serve warm or at room temperature, topped with the blueberries.

Make Ahead Tips

The blueberries in their syrup will keep, covered and refrigerated, for 1 day; the thyme flavor will become more intense. Reheat gently just before serving.