3/4 cup unsalted butter, room temperature, plus more for pan
2 cup all-purpose flour, plus more for pan
2 cup granulated sugar
2 large eggs
2 egg yolks
1 tsp baking powder
2/3 cup whole milk
2 tsp vanilla extract
confectioners’ sugar, for dusting
raspberries (optional), for serving
whipped cream (optional), for serving
1. Preheat oven to 400F. Lightly butter and flour a 9-inch round cake pan (2 inches deep). In a medium saucepan, cover lemon slices with 3 cups water. Add pinch of salt, cover, and bring to a boil over high. Boil lemons, partially covered, until very tender, 15 minutes. Drain and transfer to food processor. Add butter and process until smooth, scraping down bowl as needed. Add granulated sugar, eggs, and yolks and process to combine; transfer to a large bowl.
2. In a medium bowl, whisk together flour, baking powder, and 1/2 tsp salt. Measure milk in a liquid-measuring cup and add vanilla. In two additions, add flour mixture to lemon mixture, alternating with milk.
3. Transfer batter to pan and smooth top. Bake until cake is golden brown and a toothpick inserted in center comes out with a few moist crumbs attached, 40 minutes. Let cool in pan on a wire rack, 20 minutes. Remove cake from pan and let cool completely on rack, 1 hour. (Store cooled cake, tightly wrapped in plastic, at room temperature up to 1 day.) Dust with confectioners’ sugar and serve with raspberries and cream, if desired.