Preheat the oven to 350°F and position a rack in the center. Line a baking sheet with parchment paper.
In a medium bowl, whisk together the almond flour, quick oats, cinnamon powder, baking soda, and salt until evenly combined.
In a separate large bowl, use an electric hand mixer to beat the softened butter and applesauce until combined. Add both sugars, the egg, and the vanilla extract, and beat until the mixture is smooth and well combined.
Stir the dry ingredients into the butter–sugar mixture until just combined, then fold in the raisins.
Cover the bowl and chill the dough in the refrigerator for 15 minutes to firm slightly.
After chilling, portion the dough into 1-tablespoon-sized balls and place them on the prepared baking sheet about 2 inches apart. Press each ball to about 1/3 inch thick.
Bake on the center rack for 16 to 18 minutes, until the edges are lightly golden brown and the cookies feel set.
Remove the pan from the oven and let the cookies cool completely on the pan before serving or storing.