Preheat your oven to 350°F (175°C) and grease your donut pan.
In a medium bowl, whisk together flour, sugar, baking powder, cinnamon, nutmeg, and salt until well combined.
In another bowl, mix together the pumpkin puree, milk, and egg, stirring until fully combined.
Gently fold the wet ingredients into the dry ingredients, mixing until just combined.
Using a piping bag or spoon, fill each donut cavity about 2/3 full.
Bake for 10-12 minutes, or until a toothpick inserted in the center comes out clean.
Allow the donuts to cool in the pan for 5 minutes before transferring them to a wire rack.
Once cool, glaze, sprinkle with powdered sugar, or enjoy them plain.