Roll dough into rectangle:
Gently punch down the dough and turn it out onto a lightly floured surface. If the dough was refrigerated, it will be firm. Shape it into a mound, dust the top with flour, and roll it into a rectangle 1/2 inch (1.3 cm) thick.Cut doughnut rounds:
Using a cookie cutter or jar lid, cut out rounds 3 1/2 inches (9 cm) in diameter. Place each doughnut on a piece of baking paper. Gather the scraps, knead them into a ball, let rest for a few minutes (to relax the gluten and prevent spring-back), then roll and cut again.Rest doughnuts until puffy:
Allow the doughnuts to rest for 30 to 60 minutes until they become puffy. If they appear dry, lightly brush the tops with water. Using kitchen scissors, cut around each doughnut on the baking paper so each sits on its own square.Heat oil for frying:
Shortly before frying, pour oil into a deep fryer or deep pot and heat to 340°F (170°C). Fill a shallow bowl with the coating sugar.Fry doughnuts 2 minutes per side:
Carefully lower 2 to 3 doughnuts into the hot oil, using tongs to remove the baking paper. Fry for 2 minutes until deep golden brown, then flip and fry for another 2 minutes.Monitor oil temperature:
Maintain the oil temperature, ensuring it does not exceed 350°F (175°C), or the doughnuts will brown on the outside before the centers are cooked.Coat doughnuts in sugar:
Remove the fried doughnuts with a slotted spoon and briefly place them on a wire rack. While still hot, toss them in a bowl of granulated or caster sugar to coat, then return to the rack and continue frying the remaining doughnuts.