In a small bowl, stir together the warm water or milk, yeast, and a pinch of the granulated sugar. Let stand for about 10 minutes, until foamy.

In a large mixing bowl, whisk together the remaining 1/4 cup of granulated sugar, the egg yolks, and 2 tablespoons of the oil.

Add the egg yolk mixture to the yeast.

In a large mixing bowl, combine the flour and salt. Stir the wet ingredients into the dry ingredients with a wooden spoon (or use a stand mixer with a dough hook) until they come together to form a sticky dough.

Continue to beat or knead the dough, adding a bit more flour as needed, until the dough is smooth and elastic. You'll knead it for about 5 minutes.

Coat a large mixing bowl lightly with oil then place the dough into it, turning the dough over to coat with the oil. Cover the bowl with plastic wrap and set it in a warm spot on the countertop to rise for 1 to 2 hours. The dough should double in size.

Dust your countertop workspace with flour. Turn the dough out of the bowl onto the counter and sprinkle a bit more flour over the top. Using your hands, pat the dough out into a rectangle that is about 10 inches by 12 inches and about ¼-inch thick.

Use a dough scraper or pizza cutter or a 2-inch round pastry cutter, cut the flattened dough into 2-inch squares or rounds. You should get about 24 squares or rounds.

Arrange the donuts on a parchment-lined baking sheet and cover with plastic wrap or a tea towel. Let rise a second time, until doubled in size, about 45 minutes to 1 hour.

Line a baking sheet with a few layers of paper towels and set a wire cooling rack on top.

Fill a high-sided pot (like a 2-quart saucepan) with about 3 inches of cooking oil and heat it over medium-high heat. Use a deep-fry thermometer to check the temperature. It is ready when it is around 350ºF.

Drop the dough squares into the oil 3 or 4 at a time. Cook for about 3 minutes, until the bottom half is golden brown. Flip the donuts over and cook on the second side until it is golden brown, 1 to 2 minutes more. Lift the donuts with a slotted spoon and allow excess oil to drip back into the pot.

Transfer the donuts to the cooling rack and repeat with the remaining dough squares.

If you choose to fill the donuts, fill a pastry bag fitted with a small round tip with your desired filling. Once the donuts are cool enough to handle, poke the tip of the pastry bag into a donut, pushing it about halfway in, and squeeze to deposit some of the filling. Fill each donut with about 2 teaspoons of filling. Return the filled donuts to the cooling rack over the paper towel-lined baking sheet.

Using a fine-meshed sieve, dust powdered sugar generously over the donuts, covering them on both sides.

Serve immediately.