In a medium saucepan over medium heat, melt 2 cups of unsalted butter. Stir constantly for about 5-6 minutes until the butter turns a rich golden brown and emits a delightful nutty aroma.

While the brown butter is cooling, preheat your oven to 350°F (175°C). Prepare three 8-inch or four 7-inch cake pans by lining the bottoms with parchment paper and lightly greasing the sides.

In a large mixing bowl, sift together 3 cups of all-purpose flour, 3 cups of granulated sugar, 2½ teaspoons of baking powder, and 1 teaspoon of fine salt. Whisk to distribute evenly.

Gradually add the cooled brown butter to the flour mixture. Mix with a spatula until the texture resembles moist sand.

Add 1 cup of egg whites, 1½ cups of full-fat sour cream, ¼ cup of vegetable oil, and 2 teaspoons of vanilla extract. Mix thoroughly until smooth.

Evenly divide the batter among the prepared cake pans. Bake for 33-35 minutes, or until a toothpick comes out with a few moist crumbs.

Once baked, let the cake layers cool in the pans for 10 minutes. Then transfer to a wire rack or freezer to cool completely.

To make the frosting, beat the remaining brown butter and 1 cup of cream cheese until smooth. Gradually mix in powdered sugar and heavy whipping cream until creamy.

Assemble the cake by placing one layer on a platter, frosting between layers, and coating the sides with frosting.