In the bowl of a stand mixer, whisk together warm milk, ¼ cup sugar and instant yeast. Cover and let sit for 5 minutes (it should foam up). Add melted butter, egg, egg yolk and vanilla. Whisk until combined.

Add flour, salt and nutmeg. If using a stand mixer, attach a dough hook and mix/knead on medium speed until the dough pulls away from the sides. Then transfer to a lightly floured work surface and knead 2 minutes by hand. The dough should be soft and pillow-like.

Place dough back into the bowl and cover it with a clean kitchen cloth or plastic wrap. Let dough rise for 30 minutes.

Punch the dough down and transfer to a lightly floured work surface. Roll the dough until it’s about ½-inch thick. Use a 3-inch round biscuit cutter or cookie cutter to cut the dough into circles. Place them on a parchment-lined baking sheet 2 inches apart. Cover with a clean kitchen towel and let them rest for 1 hour. For rerolling scraps, form the dough into a ball and let the dough rest for 20 minutes before rerolling.

To fry the donuts, add the oil to the fryer or a Dutch oven. You’ll need enough oil so it’s 2 inches deep. Adjust your fryer to 350 F or use a candy thermometer to test the temperature.

Add 3 to 4 donuts to the pot keeping in mind that the donuts will puff up as they cook. Cook 45 to 60 seconds per side, flipping halfway through. Make sure the outsides get a nice golden brown color.

Use a slotted spoon to transfer donuts to a plate lined with paper towels. If needed, use a toothpick or skewer to check that the donuts are cooked all the way through. Fry remaining dough.

While the donuts are still warm, gently toss them in granulated sugar.

Transfer jelly to a frosting bag with a jelly tip. Insert tip into the side of the donuts and squeeze about 2 tablespoons of jelly into each donut. Serve warm or at room temperature.