Sift the flour, sugar, baking powder, baking soda, cinnamon, and salt into a medium mixing bowl.
Cut the cold butter into ½-tablespoon pieces and add to the dry ingredients. Using a pastry blender or two forks, cut the butter in until it's broken down into pea-sized pieces.
Add the buttermilk and almond extract and stir just until a rough, shaggy dough forms.
Fold in the chopped peaches gently, without crushing them.
Turn the dough onto a lightly floured surface and divide in half. Pat each half into a circle no more than ¾ inch thick.
Score each round into wedges and lift carefully into a greased, parchment-lined air fryer basket.
Air fry at 350°F for 12 to 15 minutes, until golden and a toothpick comes out clean. Repeat with the second round.
Whisk together the powdered sugar, almond extract, and cream, adding cream gradually until it reaches a drizzling consistency. Drizzle over cooled scones and let set.