Fill a saucepan with 2" of canola or vegetable oil and warm the oil over a medium-low heat until it reaches 350°F. Use a candy thermometer to test the temperature.
Remove dough from the refrigerator and turn out onto a lightly floured surface. Using your hands or a lightly floured rolling pin, roll or pat the dough to ½" thickness. Use a doughnut cutter to cut out donuts. Role the doughnut hole scraps into smooth balls. Continue re-rolling and cutting to get as many doughnuts as possible from your dough.
Place doughnut shapes and doughnut holes onto a lined baking sheet and place in the freezer for a few minutes until your oil is fully heated.
Once oil has reached 350°F, remove baking sheet from the freezer and carefully drop doughnuts and doughnut holes into the oil, making sure not to crowd the pan.
While your first batch of doughnuts is frying, stir together sugar and cinnamon in a shallow disk.
Fry for 1 ½-2 minutes per side, using tongs to flip them in the oil, then remove from the pan and immediately coat them in the cinnamon sugar mixture. Then place on a paper towel lined plate to briefly drain.
Between batches, wait a few minutes so that the oil temeprature comes back up to 350°F.