Brown the Butter: Melt the unsalted butter in a saucepan over medium-low heat until it foams and begins to brown with nutty aroma. Let it cool completely.
Prepare Pans: Preheat oven to 350 °F (175 °C). Grease and line three 8-inch round cake pans with parchment.
Mix Dry Ingredients: In a large bowl whisk together cake flour, granulated sugar, light brown sugar, baking powder, baking soda, and salt.
Combine with Butter: Add the cooled browned butter to the dry mix and stir until incorporated.
Add Wet Ingredients: In another bowl whisk buttermilk, eggs, and vanilla. Gradually add the dry mixture to the wet, stirring gently until just combined.
Add Pecans: Fold in finely chopped pecans.
Bake: Divide batter evenly among pans. Bake ~30 minutes or until a toothpick inserted into the centers comes out clean. Cool completely.
Make Frosting: Beat softened butter, cream cheese, light brown sugar, vanilla, and salt until smooth. Gradually beat in powdered sugar and heavy cream until light and fluffy.
Assemble: Level cake layers if needed. Spread frosting between layers and over the top and sides. Decorate with additional chopped pecans if desired.