How to Make It
Preheat oven to 350°F. Beat butter with a heavy-duty stand mixer on medium speed until creamy. Gradually add granulated sugar and brown sugar, beating until light and fluffy, 3 to 5 minutes. Add eggs, 1 at a time, beating just until blended after each addition.
Whisk together flour, baking powder, cinnamon, salt, and baking soda in a medium bowl until well blended. Add flour mixture to butter mixture alternately with buttermilk, beginning and ending with flour mixture. Beat on low speed just until blended after each addition. Beat in vanilla extract. Pour batter into 3 greased (with butter) and floured 9-inch round pans.
Bake in preheated oven until a wooden pick inserted in center comes out clean, 19 to 24 minutes. Cool in pans on wire racks 10 minutes, and remove from pans. Cool completely on wire racks, about 1 hour.
Use a small offset spatula to spread Peach Buttercream between layers and on top and sides of cake. Garnish top with peach slices.