Preheat the oven to 350 degrees F. Spray muffin pan with non-stick cooking spray. Cut 1 tablespoon of butter into 12 small cubes and place one into each of the 12 muffin wells; sprinkle with ½ teaspoon of brown sugar.
Slice 1 peaches into thin slices and place about 3 slices into the bottom of each muffin pan. Cut the remaining peaches into small cubes and set aside.
In a small bowl, whisk together flour, baking powder, baking soda and salt.
In a mixing bowl with paddle attachment, beat the remaining ⅓ cup of butter and granulated sugar together until creamy. Add egg and vanilla extract and beat for another 2-3 minutes, or until well combined, scraping down the sides, as needed.
Add half of the flour mixture into the batter, beat for 1 minute. Stir in the buttermilk and beat for another minute. Add the remaining flour mixture and beat just until combined. Fold in the cubed peaches.
Divide the batter into 12 muffin pan cups. Bake for 25-30 minutes, or until inserted toothpick comes out clean.
Cool the cakes in the pan for 5 minutes; run a knife around the sides of each to loosen from the muffin tin. Place the wire rack over the muffin pan and carefully turn the pan upside down to remove the cakes. Cool completely before serving.