In a medium saucepan over medium heat, melt 1 cup of unsalted butter, stirring frequently until it turns golden brown and emits a nutty aroma, about 5–7 minutes. Remove from heat and let it cool for about 10 minutes.

In a large mixing bowl, combine the cooled browned butter and 1 cup of granulated sugar, whisking until well blended. Add in 3 large room-temperature eggs, one at a time, mixing thoroughly. Stir in 1 tablespoon of vanilla extract.

In another bowl, gently whisk together 1 ½ cups of cake flour, 1 ½ teaspoons of baking powder, and ½ teaspoon of salt. Gradually fold this dry mixture into the butter mixture, then add ½ cup of sour cream and ¼ cup of milk.

Preheat your oven to 350°F (175°C). Grease a 9-inch round cake pan with butter and dust it with flour. Pour the cake batter into the pan, smooth the top, and sprinkle sugar over the batter.

Bake the cake for 35–40 minutes, or until the top is golden brown and a toothpick inserted in the center comes out with a few moist crumbs.

Once baked, let the cake cool in the pan for about 10 minutes, then transfer it to a wire rack to cool completely. Serve as is or with fresh berries and whipped cream.