Preheat the oven to 400°F. Grease two donut pans (6 wells each) with nonstick cooking spray, or lightly grease a muffin pan.

In a medium bowl, whisk together the gluten-free flour, coconut sugar, baking powder, baking soda, 2 1/4 teaspoons apple pie spice, and salt until well combined.

In a separate bowl, stir together the apple cider, applesauce, melted coconut oil, vinegar, and vanilla extract until smooth.

Make a well in the center of the dry ingredients. Pour the wet mixture into the well and gently fold everything together with a spatula until a thick batter forms.

Spoon the batter into a piping bag or a resealable plastic bag with a corner cut off. Pipe the batter into the prepared donut wells, filling each about 3/4 full. You should have enough for 12 donuts.

Bake on the center rack for 9 to 11 minutes, checking at 8 minutes. The donuts are done when a toothpick inserted in the center comes out clean.

While the donuts bake, mix the white sugar and remaining 2 teaspoons apple pie spice in a shallow bowl. Melt a few tablespoons of extra coconut oil or vegan butter if you plan to dip the donuts before coating.

Let the baked donuts cool in the pan for 2 to 3 minutes. Run a small knife around each donut to loosen it, then turn the donuts out onto a wire rack.

For a light coating, toss each warm donut in the spiced sugar and set on the rack to dry. For a richer finish, dip each donut into the melted butter or oil first, then roll in the spiced sugar and return to the rack.