Beat cottage cheese and butter in a large bowl with an electric mixer until well combined with most cottage cheese curds intact, scraping down the sides of the bowl a few times.
Stir flour into butter mixture gradually with a wooden spoon just until a soft dough forms that is no longer sticky; turn dough out onto a floured surface. Bring dough together with floured hands; knead 3 to 4 turns.
Roll dough gently into a fairly thick square, fold in half, and pat to flatten again; fold dough in half again in the opposite direction. Repeat rolling and folding process 2 more times. Roll dough into an 8-inch square; divide into 4 equal portions. Wrap each portion in plastic wrap; refrigerate for 4 hours or up to overnight.
Preheat oven to 375 degrees F (190 degrees C). Line a baking sheet with parchment paper.
Roll one portion of dough out on a lightly floured surface 1/4-inch thick. Cut dough into 4-inch squares with a sharp knife; cut each square diagonally to make 2 triangles.
Roll each dough triangle from the long edge toward the triangle point to form crescent shapes; place on prepared baking sheet.
Bake in the preheated oven until golden, about 20 minutes. Remove to cool on a wire rack.
Whisk confectioners' sugar, lemon juice, and lemon zest together in a bowl until smooth; brush or drizzle lemon glaze over tops of cooled crescents.