Preheat oven to 350°F and lightly grease a donut pan.
In a large bowl, whisk together flour, cane sugar, baking powder, cinnamon, and nutmeg.
Add oat milk, vanilla extract, applesauce, and melted vegan butter. Mix 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 ¾ full.
Let the filled pan sit for 5 minutes before baking.
Bake for 15 minutes, or until the tops spring back lightly when touched.
Allow donuts to cool in the pan for a few minutes before transferring to a cooling rack. Cool completely before icing.