Preheat the oven to 350°F (175°C). In a small bowl, mix melted butter and brown sugar. Pour the mixture into the bottom of the muffin tin.

Arrange the sliced peaches evenly over the butter-sugar mixture.

In a mixing bowl, whisk together flour, baking powder, baking soda, and salt.

In another bowl, cream together the softened butter and granulated sugar until light and fluffy.

Add the eggs one at a time, mixing well after each addition. Stir in vanilla extract.

Gradually add the dry ingredients to the wet mixture, alternating with buttermilk, and mix until just combined.

Spoon the cake batter over the peaches in the muffin tin, filling each cup about 2/3 full.

Bake in the preheated oven for 20-25 minutes or until a toothpick inserted into the center comes out clean.

Let the mini cakes cool for a few minutes, then invert onto a serving plate.