Preheat your oven to 350°F (175°C).
Pour the melted butter into a 9-inch round cake pan and sprinkle the brown sugar evenly over the butter.
Arrange the peach slices over the brown sugar in a single layer.
In a medium bowl, whisk together the flour, baking powder, and salt.
In a separate large bowl, beat together the softened butter and granulated sugar until light and fluffy.
Add the eggs one at a time, beating well after each, then stir in the vanilla extract.
Gradually add the flour mixture to the butter mixture alternately with the milk, beginning and ending with the flour mixture, until just combined.
Pour the cake batter over the peaches in the pan, and smooth the top.
Bake in the preheated oven for 45 minutes or until a toothpick inserted into the center comes out clean.
Let the cake cool in the pan for 10 minutes, then run a knife around the edges to loosen and invert onto a serving plate.