On a floured work surface, roll out the dough until ½ inch (1 cm) thick. Using a round 3-inch (7.5 cm) cookie cutter, cut out the doughnuts. Using a small, round ¾-inch (2 cm) cookie cutter, cut out the doughnut holes. Reuse any dough scraps. Let rest for 15 minutes at room temperature to allow the dough to dry out slightly and form a nice crust while frying.