1. Preheat oven to 350°. Line 3 baking sheets with parchment paper.
2. In a medium bowl, combine whole-wheat flour, almond flour, salt, and baking soda. In a large bowl, beat butter with sugar until creamy; beat in egg, applesauce, and almond extract. Stir in dry ingredients until combined, then stir in cherries and almonds.
3. Spoon dough by heaping teaspoons onto prepared baking sheets, 2 inches apart. Bake 15 minutes, until golden. Cool on pans 2 minutes; transfer to wire racks.