Preheat the oven to 180°C (350°F) and lightly spray a 6-hole doughnut pan with cooking oil.
In a medium bowl, sift together the flour, baking powder, cinnamon, nutmeg, and salt. Stir gently with a spatula to combine.
In a large bowl, whisk together the egg, sugar, and vanilla extract. Add the oil and whisk until combined.
Gradually add the dry ingredients to the wet mixture, whisking gently. Slowly pour in the dairy free milk, whisking until the batter is smooth.
Transfer the batter into a large piping bag or a ziplock bag with the tip cut off. Pipe the batter into the doughnut pan, filling each cavity about halfway.
Place in the oven and bake for 8-10 minutes, or until the tops spring back when lightly touched. Let the doughnuts cool in the pan for 2 minutes before turning them out onto a wire rack.
In a small bowl, mix together the sugar and cinnamon. In another small bowl, melt the dairy free butter.
Once cool enough to handle, use a pastry brush to brush each doughnut with the melted dairy free butter, ensuring an even coating. Then, roll in the cinnamon sugar mixture until fully coated.
These doughnuts are best enjoyed fresh. You can store any leftovers in an airtight container at room temperature for up to 2 days.