Preheat your oven to 350°F (175°C) and line a cupcake pan with liners. Set aside.
Place the butter in a saucepan over medium heat and allow it to melt completely.
Continue cooking, stirring occasionally, as the butter begins to foam and bubble.
Watch closely as small brown specks form at the bottom of the pan and the butter develops a warm, nutty aroma.
As soon as the butter turns a deep golden color, remove it from the heat and immediately pour it into a heat-safe bowl to prevent burning.
Let the butter cool until it is no longer hot but still in liquid form
In a large mixing bowl, whisk together the cooled brown butter and granulated sugar until smooth and slightly thickened.
Add the eggs one at a time, mixing well after each addition until fully incorporated. Then, stir in the vanilla extract.
In a separate bowl, whisk together the flour, baking powder, and salt.
Add the dry ingredients to the batter in three additions, alternating with the buttermilk. Begin and end with the dry ingredients, mixing gently after each addition.
Fill each liner about three quarters full with batter.
Bake for 18 to 20 minutes, or until the tops spring back lightly when touched and a toothpick inserted into the center comes out clean.
Remove the cupcakes from the pan and allow them to cool completely before frosting.