Activate the Yeast: In a bowl, mix the warm milk, sugar, and yeast. Let it sit for 5-10 minutes until it becomes foamy.
Prepare the Dough: In a large mixing bowl, combine the flour, salt, nutmeg (if using), and vanilla extract. Add the yeast mixture, egg, and softened butter. Mix and knead until the dough is smooth and elastic (about 8-10 minutes). Cover and let the dough rise in a warm place for 1-1.5 hours, or until it doubles in size.
Shape the Donuts: Roll out the dough on a lightly floured surface to about 1⁄2 inch thickness. Use a heart-shaped cookie cutter to cut out hearts. If you wish to make classic donut holes, use a small round cutter. Place the hearts on a parchment-lined tray, cover, and let rise for another 30 minutes.
Fry the Donuts: Heat oil in a deep pot to 350°F (175°C). Fry the donuts in batches for about 1-2 minutes per side until golden brown. Remove and drain on paper towels.
Coat with Sugar: Brush the warm donuts with melted butter, then roll them in sugar—or cinnamon sugar for an extra flavor kick.
Serve & Enjoy! Enjoy them warm, or add a sweet filling like jam, chocolate, or custard for a delightful surprise!