Preheat oven to 350°F and lightly grease a donut pan.
In a large bowl, whisk together the flour, sugar, baking powder, cinnamon, and nutmeg.
Add the oat milk, vanilla extract, applesauce, and melted vegan butter. Stir until just combined. Do not overmix.
Transfer batter to a piping bag or zip-top bag with the corner cut. Pipe batter into donut cavities, filling about three-quarters full.
Let the filled pan rest for 5 minutes before baking.
Bake for 15 minutes, or until lightly golden and the tops spring back when touched.
Cool in the pan for a few minutes, then transfer to a wire rack and allow donuts to cool completely.