1. Place rack in middle of oven and preheat to 375°F. Line a 9-inch square baking pan with foil, allowing a 3-inch overhang on 2 sides. Butter foil and pan.
2. In a bowl, mix 1/4 cup sugar and cinnamon. In a large bowl, whisk flour, baking powder, baking soda and salt.
3. Using an electric mixer on medium speed, beat butter with 1 cup sugar until light, about 3 minutes. Scrape down bowl with a spatula and mix in ground almonds and almond extract. Add eggs, one at a time, beating well after each addition.
4. Reduce mixer speed to low. Add flour mixture in 3 batches, alternating with buttermilk, beginning and ending with flour. Mix until just combined.
5. Spread batter evenly in pan; arrange peaches on top in 4 rows. Sprinkle cinnamon-sugar and sliced almonds on top. Bake until cake is golden on top and a toothpick inserted into center comes out clean, 45 to 50 minutes. Let cool in pan on a wire rack. Use foil handle to remove cake; serve at room temperature.