Blend the cottage cheese in a small blender or food processor until completely smooth.
In a large bowl, rub the lemon zest into the sweetener with your fingertips for 30 seconds to release the oils. Add the butter and beat until creamy, then beat in the blended cottage cheese, egg yolk, lemon extract, and vanilla.
In a separate bowl, whisk together the almond flour, baking powder, xanthan gum, and salt. Stir into the wet mixture until a soft dough forms, then chill for 30 minutes.
Preheat the oven to 350°F and line a baking sheet with parchment paper. Roll the dough into 1 1/2 tbsp balls and flatten each to about 1/2 inch thick.
Bake for 12 to 14 minutes, until the edges are lightly golden. Cool on the baking sheet for 15 minutes, then move to a wire rack and cool completely.
Whisk the powdered sweetener, lemon juice, and lemon zest until smooth and thick. Spoon the glaze over the cooled cookies and let it set for 20 minutes before serving.