Activate the YeastIn a large bowl, mix together the warm milk, yeast, and 1 tablespoon of the sugar. Let sit for 5-10 minutes until foamy. If there’s no foam, the yeast might be inactive, so try again with fresh yeast.
Prepare the DoughAdd the remaining sugar, eggs, melted butter, salt, and nutmeg to the yeast mixture. Stir to combine. Gradually add the flour, one cup at a time, mixing until a sticky but smooth dough forms.
Knead the DoughTurn the dough onto a floured surface and knead for 5-7 minutes until it’s soft and elastic. If it’s sticking, add a little more flour as you go.
First RisePlace the dough in a greased bowl, cover with a damp towel, and let it rise in a warm place for 1-1.5 hours, or until it has doubled in size.
Shape the DoughnutsRoll out the dough on a floured surface to about 1/2-inch thickness. Use a 3-inch cutter for the doughnuts and a 1-inch cutter for the holes. Transfer the cut doughnuts to a parchment-lined baking sheet.
Second RiseCover the doughnuts with a towel and let them rise for another 30 minutes until they’re puffy.
Fry the DoughnutsHeat 2-3 inches of vegetable oil in a deep pot to 350°F. Fry the doughnuts a few at a time, about 1 minute per side, until golden. Use a slotted spoon to transfer them to a wire rack to drain.
Make the GlazeWhile the doughnuts are cooling slightly, whisk together powdered sugar, milk, and vanilla extract until smooth. Dip each warm doughnut into the glaze, allowing excess to drip off.
ServeEnjoy the doughnuts warm for the best flavor and texture. They’re perfect fresh out of the glaze, with a crackly, sweet finish!