Preheat the oven to 350°F (175°C).

Grease the donut pan with cooking spray or butter.

In a mixing bowl, combine the flour, sugar, baking powder, salt, and nutmeg.

In another bowl, whisk together the milk, melted butter, egg, and vanilla extract.

Pour the wet mixture into the dry ingredients and stir until just combined.

Spoon the batter into the prepared donut pan, filling each cavity about 2/3 full.

Bake in the preheated oven for about 10 minutes, or until a toothpick comes out clean.

Let the donuts cool in the pan for a few minutes before transferring them to a cooling rack.