In a small bowl, combine warm milk, sugar, and yeast. Stir and let it sit for 5–10 minutes until it becomes frothy.
In a large mixing bowl, combine flour, salt, and nutmeg. Add the yeast mixture, egg, vanilla, and softened butter. Mix to form a soft dough.
Knead the dough on a floured surface for 8–10 minutes until smooth and elastic. Place it in a greased bowl, cover with a clean cloth, and let it rise in a warm place for 1 hour or until doubled in size.
Punch down the risen dough and roll it out to about ½-inch thickness. Cut into strips about 8 inches long and 1 inch wide. Take each strip and twist it, then coil it into a round spiral shape (like a twisted snail shell). Pinch the end underneath to seal.
Place shaped doughnuts on a tray, cover loosely, and let them rise again for 30–45 minutes.
Heat oil in a deep pan over medium heat (about 170–180°C or 340–355°F). Fry doughnuts in batches, turning once, until golden brown on both sides.
Remove and drain on paper towels. While warm, roll in sugar or glaze if desired.
