Preheat your oven to 350 degrees. Line two muffin tins with paper liners and set aside.
Whisk together the flour, baking powder, baking soda, and salt in a medium sized bowl. Set aside.
Cream together the butter and sugar in the bowl of an electric mixer until light and fluffy. Add the egg, vanilla, and peach schnapps until fully combined. Slowly add the milk and puree and continue to stir until smooth. Fold in the dry ingredients.
Fill the liners 3/4 full. Bake 15-20 minutes or until a toothpick comes out clean. Cool on a wire rack.
Filling:
Puree the peaches in a blender until smooth. Pour into a saucepan with the sugar and bring to a boil.
Whisk together the water and cornstarch. Stir into the fruit mixture and continue to cook for 5 minutes or until slightly thickened. Let cool completely and fill cupcakes.*
Frosting:
Whip the butter with an electric mixer until light and fluffy. Slowly stir in the powdered sugar, vanilla, and cream. Whisk until light and fluffy and fully combined, making sure to scrape the sides of the bowl. Stir in the cinnamon.