Heat oven to 325 degrees F. Line two baking sheets with parchment.
Stir together almond flour, granulated sugar, cocoa and salt in a large mixing bowl.
In a small bowl, put egg whites and almond extract. Beat with a fork until frothy.
Add egg white mixture to almond flour mixture, and stir well with a large spoon or spatula to form a sticky dough.
Use a teaspoon to scoop a walnut-sized blob of dough. Gently roll between palms into a 1-inch round. Toss lightly in a bowl of granulated sugar, then generously in a bowl of powdered sugar to coat well. Repeat with the rest of the dough. Place on parchment paper 2 inches apart; there should be 12 cookies per sheet. Push a dried cherry in the center of each cookie.
Bake on the center rack until a thin crust has formed and the surface is crinkly, 15 to 20 minutes. Do not overbake - the goal is a chewy center. Repeat with the rest of the dough until all of the cookies are baked. Let cool, and serve.