While the dough is chilling or about 20 minutes before you plan to cut out the donuts, pour the oil into a large dutch oven and place a candy thermometer on the side of the pot.
Place a wire rack into a baking sheet and set it next to the stove for the fried donuts to sit on.
Place the pot over low heat if using a gas stove and medium low if electric.
Keep an eye on the oil temp but let it heat up to 350 F.
Once the dough has chilled, roll it out on a well floured surface with a piece of parchment paper on top. Be sure to scoot the dough around on the counter between rolls to keep it from sticking.
Roll the dough out so that it is 1/2" thick.
Use a biscuit cutter or a glass that is 4" inches in diameter and cut out 4-5 donuts. Use a smaller circle that's about 1" in diameter to cut out the donut holes.
Place the donuts and donut holes on a parchment lined sheet and place in the fridge until the oil is hot. Scraps can be cut into additional donut holes but I don't recommend re-rolling the dough.
Once the oil has reached 350 F. Carefully place two of the donuts in the oil, dropping them away from you. Set a timer for 2 minutes and keep an eye on the oil temperature. It should stay between 340 and 350.
At first the donuts will sink, and then they'll float, and then they will start to puff and get that classic crack around the top.
Once the two minutes are up and the tops have cracked, use a metal slotted spoon or spider to carefully flip them over, away from you so the oil doesn't splash on to you.
Fry for another two minutes.
Use the same metal tool to scoop the donuts out one at a time and place them on the wire rack to allow excess oil to drip off.
Let the oil come back to 350 before adding in the second round of donuts. Then repeat the frying steps above. Lastly fry the donut holes and scraps for about 1 minute on each side.