In a large bowl, whisk together flour, sugar, baking powder, salt, and nutmeg (if using).
In a separate bowl, whisk together the milk, eggs, melted butter, and vanilla extract.
Add the wet ingredients to the dry ingredients and stir until just combined. The dough should be soft and slightly sticky.
Shape the Donuts:
Lightly flour a clean surface and turn the dough out. Gently knead the dough a few times to bring it together.
Roll the dough to about 1/2-inch thickness.
Use a donut cutter or two round cookie cutters to cut out the donuts.
Fry the Donuts:
In a deep pot or skillet, heat about 2 inches of vegetable oil over medium heat. Use a thermometer to keep the temperature around 350°F (175°C).
Carefully drop the donuts into the hot oil, a few at a time, being cautious not to overcrowd the pan. Fry until golden brown on both sides, about 1-2 minutes per side.
Use a slotted spoon to remove the donuts and transfer them to a paper towel-lined plate to drain.
Optional Glaze:
In a small bowl, whisk together powdered sugar and milk (or vanilla extract) to make a glaze.
Dip each donut into the glaze while still warm, and let the excess drip off.
Serve:
Enjoy your soft, tender donuts fresh from the fryer, dusted with powdered sugar or glazed to perfection!
