In a medium bowl, whisk together flour, starch, flax meal, baking powder, baking soda, salt and spices; set aside.
In a large bowl, whisk together applesauce, maple syrup, apple cider vinegar, milk, and melted fat. Add dry ingredients to wet and whisk until well combined. Cover bowl with plastic wrap and refrigerate for 1 hour.
Preheat oven to 350° F. Liberally coat cavities of a 6-count doughnut pan with fat of choice; set aside.
Spoon batter into a pastry bag, snip corner to make a ½-inch opening and pipe into prepared doughnut pan, filling each cavity three-quarters full. Bake for 13-14 minutes, or until lightly golden brown and doughnuts spring back when pressed gently with your finger. Cool doughnuts in pan on a wire rack for 10 minutes. Carefully invert pan to remove doughnuts.
To make the apple glaze, whisk together all ingredients until smooth. If necessary, add more sugar to thicken or more juice to thin the glaze. Spoon over doughnuts.
If desired, make a crumb topping by crumbling up one of the baked doughnuts, placing on a baking sheet, and toasting at 350°F for 3-5 minutes. Sprinkle onto the remaining doughnuts.