1. Preheat your oven to 350°F (175°C) and grease a muffin tin or line it with paper liners.
2. In a small saucepan, melt the 1/4 cup of butter and stir in the brown sugar until dissolved. Spoon a tablespoon of this mixture into the bottom of each muffin cup, then arrange peach slices over the sugar mixture.
3. In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.
4. In a large bowl, cream the softened butter and granulated sugar until light and fluffy, about 3-4 minutes.
5. Beat in the eggs one at a time, followed by the vanilla extract.
6. Add the dry ingredients to the wet mixture alternately with the sour cream, beginning and ending with the flour mixture. Mix until just combined.
7. Spoon the batter over the peaches in each muffin cup, filling about three-quarters full.
8. Bake for 20-25 minutes, or until a toothpick inserted into the center of a cake comes out clean.
9. Let the cakes cool in the pan for 5 minutes, then carefully invert onto a wire rack to cool completely.

Remember, as Mama Lou used to say, patience is key—allowing the cakes to cool slightly before inverting helps them hold their shape beautifully.