Preheat your oven to 325 °F (165 °C). Lightly grease a 12-cavity donut pan with nonstick spray or softened butter.
In a large bowl, whisk together flour, sugar, baking powder, salt, and nutmeg until well blended.
In a separate bowl, whisk milk, eggs, vanilla extract, and melted butter until smooth.
Pour the wet ingredients into the dry ingredients and stir gently until just combined—do not overmix.
Transfer the batter to a piping bag or a resealable plastic bag with the tip snipped off.
Pipe the batter evenly into each donut well, filling about three-quarters full.
Bake for 10–12 minutes, or until the donuts are golden brown and a toothpick inserted comes out clean.
Allow the donuts to cool in the pan for 5 minutes, then transfer them to a wire rack.
Serve plain, glaze with your favorite icing, or roll in cinnamon sugar while still warm.