Melt 2 cups of unsalted butter in a light-colored saucepan over medium heat, stirring constantly until golden brown and nutty, about 5-6 minutes. Let cool before incorporating.

Preheat your oven to 350°F (175°C). In a large bowl, combine 3 cups of flour, 3 cups of sugar, 2.5 tsp of baking powder, and 1 tsp of salt. Gradually add the cooled brown butter and mix well.

Add 1 cup of egg whites, 1.5 cups sour cream, 1/4 cup vegetable oil, and 2 tsp vanilla extract; blend until smooth and creamy.

Divide the batter among the prepared pans: 450g for four layers or 600g for three layers. Bake for 33-35 minutes until a toothpick comes out clean.

After baking, cool the cakes in their pans for 10 minutes, then invert onto wire racks and freeze for 30 minutes.

In a mixing bowl, beat room-temperature brown butter until creamy. Add 1 cup of cream cheese and mix. Gradually incorporate 6 cups of powdered sugar, 1 tsp salt, and 3 Tbsp heavy cream until smooth.

Stack the cooled cake layers, spreading cream cheese frosting between layers and over the top and sides of the cake.