1. Prepare the Peach Topping: In a small saucepan, melt the butter over medium heat. Add the brown sugar and water, stirring until the sugar dissolves and the mixture is smooth. Bring to a gentle simmer and cook for 2-3 minutes, or until slightly thickened. Remove from heat. Divide the caramel mixture evenly among the bottoms of 12 greased muffin cups. Arrange the peach slices in a single layer over the caramel in each cup.

2. Prepare the Cake Batter: In a medium bowl, whisk together the flour, baking powder, and salt. In a large bowl, cream together 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 dry ingredients to the wet ingredients, alternating with the milk, beginning and ending with the dry ingredients. Mix until just combined, being careful not to overmix.

3. Assemble and Bake: Spoon the cake batter evenly over the peach slices in each muffin cup, filling each about two-thirds full. Bake in a preheated oven at 350°F (175°C) for 20-25 minutes, or until a wooden skewer inserted into the center of a cake comes out clean. The tops of the cakes will be golden brown.

4. Cool and Serve: Let the cakes cool in the muffin tin for 5-10 minutes before carefully inverting them onto a wire rack. If any peaches stick to the bottom of the tin, gently remove them and place them back on top of the cakes. Serve warm or at room temperature. These are especially delightful with a dollop of whipped cream or a scoop of vanilla ice cream.