3/4 cup (1 and 1/2 sticks) unsalted butter, room temperature, plus more for pan
2 cups flour, plus more for pan
4 lemons, ends removed, cut into thin slices
2 cups granulated sugar
2 large eggs plus 2 egg yolks
1 teaspoon baking powder
2/3 cup whole milk
2 teaspoons pure vanilla extract
confectioners' sugar, for dusting
raspberries and whipped cream, for serving
Preheat oven to 400 degrees. 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 a 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.
In a medium bowl, whisk together flour, baking powder, and 1/2 teaspoon salt. Measure milk in a liquid measuring cup and add vanilla. In two additions, add flour mixture to lemon mixture, alternating with milk. 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 wire rack, 20 minutes. Remove cake from pan and let cool completely on rack, 1 hour.
Dust with confectioners' sugar and serve with raspberries and cream.