Thaw puff pastry as recommended or fridge overnight (for those of us who are impatient like me, I put them on a metal sheet on top of a warm oven and flip a few times until soft).
Beat an egg. The egg will be used to fuse the 2 puff pastry sheets together.
On a floured surface, roll out both puff pastry sheets to about 11 inches. It shouldn't be too thin, but about 2/3s of original thickness.
Brush the egg on one of the puff pastry sheets. Place the second sheet on top, and roll them a bit more so they stick together.
Use a pint glass to cut out about 9 circles. You can use a piping tip bottom to cut out the middle holes. For donuts to be filled with jelly or cream, do not cut out the middle hole (read the next note for filled donuts).
Combine the dough that is left over and roll it back out into a sheet. Cut out as many donuts as you can. Repeat if possible! Note: I recommend using the second rolled out dough for filled donuts. It works well for holed donuts too. But if you are making both holed and filled, the first round I suggest cutting out the holes and the second round of rolled out dough for the filled This is because the cavity that is created is better and isn't separated at the 2 sheets. In a heavy bottom pot, like a dutch oven, heat about an inch and a half of oil.
The oil has to get HOT or else you will get mushy light oily dough. You can dip a wooden spoon end into the oil to check for the temperature. If big bubbles form very quickly, your oil is ready.
Drop in 2-3 donuts at a time. They should first sink and then float up pretty quickly. Once the bottom is browned turn them around. This is when they should start puffing up.
Once they get the color you prefer take them out with tongs onto a paper towel.