In a light-colored saucepan, melt the unsalted butter over medium-low heat until it turns a deep amber color and emits a nutty aroma, about 5-7 minutes. Remove from heat and let cool.

Preheat your oven to 175°C (350°F). Grease three 20-cm round cake pans with butter or non-stick spray and line with parchment paper.

In a large mixing bowl, whisk together cake flour, granulated sugar, light brown sugar, baking powder, baking soda, and salt.

Add the cooled browned butter to the bowl of dry ingredients and mix until it resembles coarse sand, about 2-3 minutes.

In a separate bowl, whisk together buttermilk, eggs, and vanilla extract until well blended. Gradually add to the dry mixture, mixing gently until just combined.

Gently fold in finely chopped pecans using a spatula until evenly distributed.

Divide the batter evenly among the prepared cake pans. Bake for approximately 30 minutes, or until a toothpick comes out clean.

Allow the layers to cool in their pans for 15-20 minutes, then transfer to wire racks to cool completely.

Beat together softened cream cheese, some cooled butter, light brown sugar, vanilla extract, and a pinch of salt until smooth. Gradually add confectioners' sugar and mix in heavy cream until desired consistency is reached.

Level the tops of the cooled cake layers. Spread frosting on the first layer, repeat with the second layer, and top with the final layer. Frost the top and sides of the cake, then chill to set.