Preheat your oven to 320°F and line a baking sheet with parchment paper.
Strain your cottage cheese with the cheese cloth. You should have 3/4 cup when finished.
Toss the wet ingredients (cottage cheese, pumpkin purée, egg, vanilla) into a blender or food processor—blend until completely smooth (no curds!). Set aside.
In a large bowl, whisk together all the dry ingredients until well combined.
Fold the wet mixture into the dry—stir gently until you have a thick dough. Let it sit for 10 minutes (it’ll firm up a bit).
Using a cookie scoop (or spoon), drop 24 mounds onto the parchment-lined sheet—flatten slightly if you like thinner cookies.
Bake for 20 minutes or until the edges are golden and the centers feel set. They’ll firm up more as they cool.
While they cool, whip up the frosting: beat the cream cheese, powdered sweetener, vanilla, heavy cream, and pumpkin spice extract until fluffy.
Frost the cooled cookies, and enjoy.