Preheat the oven to 350 degrees F. Line a baking sheet with parchment or a silicone baking mat.
Combine the sugar and cinnamon in a small bowl. Form the dough scraps into a ball and roll to 1/4 inch thick. Brush with the melted butter and sprinkle with the cinnamon sugar. Cut into shapes with cookie cutters, such as a 2-inch star cutter, and transfer to the prepared baking sheet.