Step 1: Brown the Butter

To make the brown butter, place the unsalted butter in a medium saucepan over medium heat. Allow the butter to melt completely, stirring occasionally. Continue to cook the butter, stirring occasionally, until it turns a golden brown color and develops a nutty aroma. This process usually takes about 5-7 minutes. Once the butter has browned, remove the pan from the heat and let it cool slightly.

Step 2: Prepare the Dry Ingredients

While the butter is cooling, prepare the dry ingredients. In a medium bowl, whisk together the all-purpose flour, baking powder, and salt.

Step 3: Beat the Eggs and Sugar

In a large bowl, beat the granulated sugar and eggs until light and fluffy, using an electric mixer on medium-high speed. This should take about 3-4 minutes.

Step 4: Add the Dry Ingredients and Buttermilk

Add the dry ingredients to the egg mixture, alternating with the buttermilk, starting and ending with the dry ingredients. Mix well after each addition until the batter is smooth.

Step 5: Fold in the Brown Butter

Finally, fold in the brown butter until it is fully incorporated into the batter.

Step 6: Bake the Cake

Preheat your oven to 350°F. Grease a 9-inch cake pan with butter and dust it lightly with flour. Pour the cake batter into the prepared pan and smooth the top with a spatula.

Bake the cake for 40-45 minutes or until a toothpick inserted into the center comes out clean. Remove the cake from the oven and let it cool for 10-15 minutes in the pan. Then, transfer it to a wire rack to cool completely.