Preheat oven to 350 degrees. Spray 2 (6 doughnuts each) doughnut pans with cooking spray and sprinkle with some almond flour. Tap out the excess flour.
In the bowl of a food processor fitted with a steel blade, combine the almond flour, baking soda, salt, cinnamon, and nutmeg. Pulse a few times to combine. Add the remaining doughnut ingredients and process until smooth. Scrape the dough into a large food storage bag, snip off about ½ inch from one corner and pipe the batter into the prepared pans filling each hole almost full. Bake for 15 minutes or until the doughnuts spring back when touched lightly and a toothpick inserted into the center comes out clean. Let cool in the pans for 5 minutes then remove the doughnuts to a wire rack to finish cooling.
Put the coconut sugar and tapioca starch in a clean coffee or spice grinder (or in a high powdered blender) and process until it looks like powder. Put into a bowl, stir in the cinnamon and vanilla. Stir in some almond milk, one tablespoon at a time, until it turns into a thick glaze.
Place a piece of waxed or parchment paper under the cooling rack and drizzle the glaze onto the doughnuts.