Preheat your oven to 350°F (175°C). Grease a 9-inch round cake pan.
Pour the melted butter into the cake pan and sprinkle the brown sugar evenly over the butter. Arrange the peach slices on top.
In a medium bowl, whisk together the flour, baking powder, and salt. Set aside.
In a large bowl, cream the softened butter and granulated sugar until light and fluffy. Beat in the eggs one at a time, then stir in the vanilla extract.
Gradually add the flour mixture to the butter mixture, alternating with the milk, beginning and ending with the flour mixture. Mix until just combined.
Pour the batter over the peaches in the cake pan, spreading it evenly.
Bake for 40 minutes, or until a toothpick inserted into the center comes out clean.
Let the cake cool in the pan for 10 minutes, then invert it onto a serving plate. Serve warm or at room temperature.