2 tablespoons vegetable oil, in addition to about 2 quarts (2 liters) for frying
1 teaspoon vanilla extract
About 1 cup filling (you can use jam, pudding or custard, Nutella, pudding, pumpkin butter, apple butter, dulce de leche, pie fillings, ), but this too is optional. I used lemon curd, Nutella, pumpkin mousse, and raspberry jam
Mix the warm water and yeast in a glass bowl and let sit until foamy, about 5 minutes.
In a separate, large bowl, mix the flour, powdered sugar, salt, and nutmeg. Whisk to combine and set aside.
Add the egg yolks, 2 tablespoons of oil, and vanilla to the water/yeast mixture and whisk until combined.
Add the liquid mixture to the flour mixture and stir with rubber spatula until the dough comes together. It should be somewhat Cover the bowl with plastic wrap and let the dough rise until doubled in size, about 1 to 2 hours.
Line a baking sheet with a few layers of paper towels. Line another baking sheet with parchment paper and dust heavily with flour. Dust a clean countertop and your hands with flour. Put the dough on the counter and dust with flour. Pat the dough into 1/4-in-thick rectangle (it should be about 10 x 12-inches in size), making sure the bottom doesn’t stick (add more flour to the counter and hands as needed). Using a pizza wheel or very sharp knife, cut the dough into 24 two-inch squares (or use a round cookie cutter if you prefer rounds) and transfer to the floured baking sheet, leaving a little space between the squares. Sprinkle the squares lightly with flour.
Add oil to a large Dutch oven or heavy pot to measure about 2 inches deep. Heat over medium to 350°F/176°C. Place 6 dough pieces in the oil and fry until golden brown, about 5 minutes on each side. Using a slotted spoon, transfer the donuts to the paper towel-lined baking sheet. Repeat with the remaining donuts.
When the donuts are cool enough to handle, use a paring knife to puncture the side of each to form a pocket in the center. Place the tip of a squeeze bottle or piping bag into the pocket and squeeze 1 to 2 teaspoons of filling into the pocket. (You can also serve the filling on the side.)
Using a fine sieve, dust the donuts with powdered Serve warm.