Whisk flour, cornmeal, baking powder, salt and cayenne in a medium bowl. Stir in Cheddar.Advertisement
Puree cottage cheese in a food processor. Add oil and process until smooth. Add the flour mixture and pulse just until the dough clumps together.
Turn the dough out onto a lightly floured surface and knead gently several times. Divide in half, form each piece into a disk and wrap in plastic wrap. Refrigerate for at least 20 minutes or up to 2 days.
Meanwhile, preheat oven to 400 degrees F. Coat 2 baking sheets with cooking spray.
Roll dough out on a lightly floured surface to a thickness of 1/8 inch. Cut out cookies, using a 2 1/2-inch round serrated or other decorative cookie cutter. Arrange on prepared baking sheets. (Reroll and cut scraps.) Bake the shortbread, 1 sheet at a time, until golden and firm, 8 to 12 minutes. Transfer to a wire rack to cool.
Make Ahead Tip: Prepare through Step 3; cover and refrigerate for up to 2 days.
(per 2 pieces): 1/2 starch, 1 fat