Preheat the oven to 350°F (175°C). Spray a muffin tin with nonstick cooking spray.
Divide the cold butter (2 tablespoons) into 12 small cubes and place them evenly in the muffin tin. Add 1/4 cup of light brown sugar to each muffin cup.
Peel and slice the peaches, aiming for about 4 slices per muffin tin. Dice any remaining peach pieces and set them aside for the cake batter.
In a stand mixer, cream together 1/3 cup softened butter, 1/2 cup granulated sugar, and 1/4 cup light brown sugar for 3 minutes, until light and fluffy.
Add 1 large egg and 2 teaspoons vanilla extract to the creamed mixture, mixing until well combined.
In a separate bowl, whisk together 1 1/4 cups all-purpose flour, 1 teaspoon baking powder, 1/4 teaspoon salt, and 1 teaspoon cinnamon.
Gradually add the dry ingredients to the wet mixture, alternating with 1/2 cup milk. Mix until just combined.
Gently fold in the diced peaches, being careful not to overmix the batter.
Carefully divide the batter evenly among the 12 muffin cups, filling each about 2/3 full.
Bake for 20-24 minutes, or until the cakes are golden brown and a toothpick inserted comes out clean. Let the cakes cool in the tin for 5 minutes, then flip the tin onto a wire rack to release the cakes.