Preheat your oven to 350°F (175°C). Grease and flour two 9-inch round cake pans.

In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.

In a saucepan over medium heat, melt 1 cup of butter. Continue cooking, stirring frequently, until the butter turns golden brown and has a nutty aroma, about 5-7 minutes. Remove from heat and let cool slightly.

In a large mixing bowl, combine the brown butter and granulated sugar. Beat with an electric mixer on medium speed until well combined. Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract.

Gradually add the dry ingredients to the butter mixture, alternating with the buttermilk. Begin and end with the dry ingredients, mixing until just combined.

Divide the batter evenly between the prepared cake pans. Bake for 25-30 minutes, or until a toothpick inserted in the center comes out clean. Let the cakes cool in the pans for 10 minutes, then transfer to wire racks to cool completely.

For the frosting, melt 1 cup of butter in a saucepan over medium heat until browned. Remove from heat and let cool slightly. In a large bowl, beat the brown butter with an electric mixer, gradually adding the powdered sugar and vanilla extract. Add heavy cream one tablespoon at a time until you reach your desired consistency.

Once the cakes are completely cool, place one layer on a serving plate. Spread a layer of frosting on top, then place the second layer on top and frost the top and sides of the cake.