Defrost puff pastry overnight in the fridge or on the counter according to package directions.
Unroll one sheet of the puff pastry on a lightly floured surface and brush the entire open side with 1/2 of the beaten egg wash.
Fold the pastry sheet back up along the seams, then repeat with the other sheet of pastry dough.
Using biscuit or dough cutters, cut out three circles from each sheet of prepared puff pastry, then a smaller hole in the center for the hole.
Whisk together the sugar and cinnamon in a large shallow bowl and set aside.
Heat the oil in a dutch oven or deep sauce pan over medium-high heat; you want the oil to be 350-375 degrees F. (If you have a candy thermometer, use it.)
Once the oil is ready, fry the donuts (and donut holes!) in batches, depending on the size of your pan. The donuts should sizzle when they touch the oil; if they don't, it's not hot enough.
Remove the donuts once golden brown, then sprinkle with cinnamon sugar mixture. Serve immediately! These taste best right out of the fryer, so don't wait around too long to enjoy them.