Cut the remaining peaches into small cubes. You should get about 1 cup of cubed peaches. Set aside.
In a small bowl, whisk together flour, baking powder, baking soda and salt.
In a mixing bowl with paddle attachment, beat butter and sugar together until fluffy and creamy, about 2 minutes.
Add egg and vanilla extract and beat it for another 2-3 minutes, or until well combined. The mixture should be fluffy and white. (Note: It's totally normal for the mixture to curdle right after adding egg, but keep mixing and it'll turn nice and fluffy!)
Add half of the flour mixture into the batter, beat for 1 minute on low speed.
Stir in the buttermilk and beat for another minute.
Add the remaining flour mixture and beat just until combined. Don't overmix the batter, or it'll make tough cake.
Fold in the cubed peaches.
Divide the batter into 12 muffin pan cups. (TIP: This large cookie scoop makes this step super easy - one scoop of batter in each muffin cup.) Bake for 25-30 minutes, or until inserted toothpick comes out clean.
Cool the cakes in the pan for 5 minutes. Then carefully run a butter knife around the edges to release the cake from the sides. Now, place a wire rack over the muffin pan and carefully turn the pan upside down to remove the cakes.
Serve the mini cakes warm with a scoop of vanilla ice cream.