Make the cupcakes: Preheat the oven to 350 degrees F. Line a 12-cup muffin pan with liners. Whisk the flour, baking powder, baking soda and salt in a medium bowl. Beat the butter and granulated sugar in a large bowl with a mixer on medium-high speed until light and fluffy, about 3 minutes. Beat in the eggs one at a time, then beat in the vanilla and almond extracts. Reduce the mixer speed to low and beat in half of the flour mixture, then the buttermilk, then the remaining flour mixture until smooth.
Divide the batter among the prepared muffin cups, filling each about two-thirds of the way. Bake until the tops of the cupcakes are lightly browned and spring back when gently pressed, about 25 minutes. Let cool 5 minutes in the pan, then transfer to a rack to cool completely.
Meanwhile, cook the peaches: Melt the butter in a large nonstick skillet over medium heat. Add the peaches and granulated sugar; cook, stirring occasionally, until the sugar dissolves and the peaches start softening, 2 to 3 minutes. Cover and continue to cook, stirring occasionally, until the peaches are soft but still hold their shape, about 5 more minutes. Remove from the heat and let cool completely.
Make the frosting: Beat the butter and confectioners' sugar in a large bowl with a mixer on medium speed until smooth. Increase the speed to medium high and beat until fluffy, 2 to 3 more minutes. Add the milk and vanilla and almond extracts and beat until smooth. Transfer to a piping bag fitted with a large round tip; pipe onto the cupcakes. Refrigerate until the frosting is firm, 20 to 30 minutes. Top each cupcake with a peach wedge.