Pour the warm milk into the bowl of an electric mixer fitted with a paddle.

Add the yeast and about 1 teaspoon of the sugar and stir once or twice.

Wait until the liquid is foamy, about 10 minutes.

Stir in 2 cups of flour on low speed.

Whisk together the eggs and egg yolk in a separate bowl until they are pale and frothy.

Whisk in the remaining sugar, vanilla extract, and salt.

Add the egg mixture to the mixing bowl.

Stir in the melted butter.

Switch the paddle to a dough hook and stir in the remaining 3 cups of flour, one cup at a time. The dough will come together around the hook. You can add up to a cup more of flour until the dough comes together. This dough is sticky, so it will be rather loose.

Transfer the dough to a bowl that has been sprayed with vegetable oil spray. Roll the dough around in the bowl to coat all sides.

Spray one side of a piece of plastic wrap and lay it, sprayed side down, onto the bowl.

Place the bowl with the dough into a warm place until it has doubled in size, about 1 hour.

Sprinkle your work surface and rolling pin with flour.

Roll out the dough to about ½-inch thick.

Use a 3-inch round cookie cutter to cut out the donuts.

Gather up the scraps and re-roll to use up the remaining dough.

Place them onto a parchment-lined baking sheet.

Cover the donuts with sprayed plastic wrap and place into a warm spot until the donuts roughly double in size, about 30 minutes more.

Heat the oil to 350° in an electric fryer, deep pot, or Dutch oven about one-third up the sides. The oil will expand as it heats and fries, so you don’t want too much oil in the pot.

Put 2 to 3 donuts into the oil, depending on the size of your pot. You want them to swim freely.

Once they are golden, use a slotted spoon to flip them and brown them on the other side. This only takes a few minutes.

Transfer the donuts to a baking sheet or cooling rack lined with paper towels.

Once they are cool enough to handle, use a squeeze bottle or a piping bag fitted with a long filling tip to gently squeeze a burst of jelly filling into the center of each donut.

Sprinkle with confectioners’ sugar.