Using a wooden spoon, stir 3-1/2 cups of the flour into the mixing bowl 1/2 cup at a time. Stir to combine everything. You want to end up with a ball of dough that you can handle that isn’t overly sticky.

Lightly flour a clean flat surface. Turn the ball of dough out onto the surface and dust the top of the ball with a little more flour. Knead the dough with the heels of your hands for about 5 minutes until it is no longer sticky and is elastic. You can add a small amount of flour if needed.

Wipe out the mixing bowl and coat it with a little vegetable oil. Place the dough into the oiled bowl and turn it once to coat the top with oil. Cover the bowl with a clean kitchen towel or plastic wrap. Place the bowl inside a turned-off oven and allow it to double in size for 60 minutes. It helps if you leave the oven light on to create a tiny amount of warmth.

Using your fist, gently punch the dough to release some of the air. Lightly dust your work surface with flour. Turn the dough out onto the floured surface and roll it out to a 1/2-inch thick disc. Using a donut cutter, cut the dough into 8 donuts and 8 donut holes. You can also use a biscuit cutter and a wide thimble if you don’t have a donut cutter. Repeat the process with any excess dough until it is all used up. Any scraps are also delicious as a fried snack for the chef.

Line a sheet pan with parchment paper. Using a spatula, carefully transfer the donuts and holes to the pan and cover them with a towel. Place the pan inside the turned-off oven and allow the donuts to rise for another 60 minutes.

Fill your Dutch oven or deep fryer with 2-inches of oil. Turn the heat to medium-high. Bring the oil to 350°F with the aid of a candy or frying thermometer.

Have a sheet pan with a wire rack insert standing by. Once the oil has come to temperature, start frying the donuts 2 or 3 at a time, flipping them over at 2 minutes. Continue to fry for an additional 1 to 2 minutes until golden brown and fluffy. Using a spider or slotted spoon, transfer the cooked donuts to the wire rack. Repeat until all the donuts are cooked and then cook the donut holes and scraps for a couple of minutes.

While the donuts are cooling, prepare the glaze. Whisk powdered sugar, milk, and vanilla together until the sugar dissolves and the glaze is a little runny but thick enough to adhere to the donuts. Adjust the ingredients as necessary to achieve the proper consistency.

When the donuts are cool enough to handle, dunk one side of each in the glaze and return them to the wire rack, glazed side up. They are ready to eat once the glaze sets.