In a large bowl, whisk together warm milk, ¼ cup sugar and instant yeast. Cover and let sit 5 minutes (it should foam up). Add melted butter, egg yolks and vanilla. Whisk until combined.
Add flour, salt and nutmeg. If using a stand mixer, attach 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. See notes for make donuts by hand.
Place dough back into the bowl and cover it with a clean kitchen cloth or plastic wrap. Let dough rise for 1 hour or until doubled in size.
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 cookie sheet 2 inches apart. Cover with clean kitchen towel and let them rest for 10 minutes.
While the donuts are resting, preheat the oven to 375 F. Bake the donuts for 10 minutes or until light golden on the tops.
Immediately brush the doughnuts with melted butter, roll in sugar and fill with jelly. I like to use a piping bag and this elongated tip to fill the donuts with jelly. Serve while still warm.
Storing jelly donuts: Store donuts in an airtight container at room temperature. Donuts are best when eaten the day they are made, but will last up to 3 days if stored properly.High altitude adjustments (Denver, CO, altitude 5,280 ft): If you are baking in a dry climate, increase milk by 1 to 2 tablespoons. Aim for a pillow-y dough, not stiff. Rising times will be shorter. The first rise only take 45 minutes.Recommended tools: