Preheat the oven to 350°F (175°C). Lightly grease your doughnut pan with butter or cooking spray.
In a large bowl, whisk together flour, sugar, baking powder, cinnamon, nutmeg, and salt.
In another bowl, whisk together milk, eggs, melted butter, and vanilla extract until smooth.
Gently fold the wet mixture into the dry ingredients until just combined. Do not overmix.
Spoon or pipe the batter into the doughnut pan, filling each cavity about three-quarters full.
Bake for 10–12 minutes or until the tops spring back lightly when touched and a toothpick comes out clean.
Let the doughnuts cool in the pan for 5 minutes, then transfer to a wire rack to cool completely.
For the glaze: whisk powdered sugar, milk, and vanilla until smooth. Add a little more milk if too thick.
Dip each cooled doughnut into the glaze. Let excess drip off, then decorate with nuts, sprinkles, or cinnamon sugar if desired.
