On a lightly floured work surface, roll dough 1/2 in. thick. Cut dough into circles with a 1½-in. cookie cutter. Arrange cookies 1 in. apart on baking sheets and chill 15 minutes.
Bake until light golden brown, 12 to 15 minutes.
Mix 1½ cups powdered sugar with 2 tbsp. fresh lemon juice and the finely shredded zest of 1 lemon. Spoon 1/2 tsp. glaze over each cooled cookie, spreading with back of spoon, and press 1 rosemary sprig into glaze. Makes 32.