1. Prepare the Dough:
In a large bowl, whisk together the flour, sugar, salt, baking powder, and nutmeg. In a separate bowl, whisk the milk, eggs, and vanilla. Add the wet ingredients to the dry ingredients and mix until just combined. Stir in the melted butter.

2. Roll and Cut:
Lightly flour a surface and roll out the dough to about 1/2-inch thickness. Use a donut cutter or a round cutter to cut out donut shapes.

3. Heat the Oil:
In a large pot or deep fryer, heat about 2 inches of oil to 350°F (175°C). Carefully drop in the donuts, frying in batches. Cook for about 1-2 minutes per side or until golden brown.

4. Drain the Donuts:
Use a slotted spoon to transfer the fried donuts to a wire rack lined with paper towels. Allow them to cool slightly.

5. Make the Chocolate Glaze:
In a medium bowl, whisk together powdered sugar, cocoa powder, milk, and vanilla extract until smooth.

6. Glaze the Donuts:
Dip the slightly warm donuts into the chocolate glaze, letting the excess drip off. Place them back on the wire rack to set.