Preheat the oven to 350°F (175°C).
Prepare a 9-inch round cake pan by greasing it with butter.
In a medium bowl, combine melted butter and brown sugar, mixing until smooth.
Spread the butter-sugar mixture evenly on the bottom of the prepared cake pan.
Arrange the sliced peaches on top of the sugar mixture.
In a large mixing bowl, beat together granulated sugar and eggs until pale and fluffy.
Add vanilla extract and bourbon to the egg mixture, mixing until incorporated.
In another bowl, whisk together flour, baking powder, and salt.
Gradually add the dry mixture to the wet mixture, combining until just mixed.
Pour the batter over the arranged peaches and smooth the top.
Bake in the preheated oven for 40-45 minutes, or until a toothpick comes out clean.
Let the cake cool in the pan for 10 minutes before inverting onto a serving plate.
Slice and serve your Bourbon Peach Upside Down Cake.