Bring all ingredients to room temperature except coconut oil, if using. Coconut oil is solid at room temperature and needs to be melted to add to this recipe. To bring eggs to room temperature more quickly, place un-cracked eggs in a bowl with very warm water while preparing other ingredients.
Peel and dice apples to a very small size (see photo - dice even finer for fewer apple chunks). Pat the pieces dry if they are very juicy. Set aside.
Whisk dry ingredients together in a small bowl. Toss the apples in the dry mixture bowl to coat, then set aside.
In a larger mixing bowl, combine wet ingredients through melted coconut oil. Once mixed, stir in the dry-apple mixture, adding the apple cider by pouring on top. Stir to combine well, but do not over-mix.
The dough should hold together easily when scooped with a spoon; if it is too dry, add more apple cider by the tablespoon until the consistency is right. Particularly juicy apples may make this dough more batter-like; if so, add a bit more gfJules Flour. Consult the video for reference about the consistency of the dough. Because of the apple chunks, this dough will not be smooth, but don't let that bother you -- the glaze will cover up any imperfections!
Preheat oven to 325° F (or 300°F convection).
Scoop out dough and roll into a log on a clean counter or pastry mat lightly dusted with gfJules Gluten Free All Purpose Flour. Score the ends of each log of dough with a fork, then dip your finger in water and touch the ends. Bring the ends together and smooth to join the dough into a round circle.
Place doughnuts or doughnut holes onto parchment-lined baking sheets or simply scoop dough into oiled doughnut pans and smooth the tops with a rubber spatula. Sprinkle with sugar and cinnamon mixture, if desired.
Bake for 10-12 minutes, testing with a toothpick for doneness (when inserted toothpick comes out clean -- not wet -- or with dry crumbs, doughnuts are fully cooked). Remove to cool on wire racks for 5 minutes, then gently roll in confectioner’s sugar or sugar and cinnamon mixture OR allow to fully cool, then dip in glaze.
To prepare the glaze, whisk maple syrup into sifted confectioner's sugar in a flat-bottomed pot over low heat on the stovetop. The pot should be at least as wide as each baked donut. It should be thin enough to easily spread but not watery. Glaze will thicken and set quickly, so you may need to keep the glaze warm while you are working.
Dip each donut top in the glaze and turn right-side-up onto parchment or wax paper to allow the glaze to drip and set.