To a small saucepan over medium-high heat, add the apple cider and apples. Bring to a boil and cook, stirring occasionally, until reduced to 2/3 cup total, about 10 minutes.
Pour the apple mixture into a medium, heat-proof mixing bowl and add the coconut oil to help it melt. Cool until lukewarm, about 20 minutes.
About 5 minutes before proceeding withthe doughnut batter, make the flax egg and preheat the oven. To make the flax egg, mix the flaxmeal and water in a small bowl. It will need to sit for 5-10 minutes.Preheat oven to 350 degrees Fahrenheit. Prepare a doughnut pan by spraying with nonstick spray, an oil mister, or lightly greasing the cups with coconut oil. Set aside.
When the apple mixture has cooled enough to proceed, add the flax egg, brown sugar, almond milk, and vanilla extract. Stir to combine.
Toa large mixing bowl, add the flour, baking powder, salt, cinnamon, nutmeg, ginger, and cloves. Stir with a whisk to combine.Add the wet ingredients to the dry ingredients and stir again, just until combined.
Spoon the batter into the cupsof the doughnut pan, or scoop the batter into a gallon-size zipper bag, snip off the end, and pipe it into the pan. Fill the cups 2/3 full, dividing the batter evenly between all the cups.
Bake until the tops spring back when you poke them, 10-12 minutes.
Remove from oven. Cool in the pan for 5-10 minutes then carefully transfer the doughnuts to a wire rack. But dont walk away just yet! Youll want to dip the doughnuts in the cinnamon-sugar mix while theyre still warm.Mix together the cinnamon-sugar topping by combining the sugar and cinnamon in a large zipper bag. One by one, gentlyplace the still-warm doughnuts in the bag with the cinnamon sugar and very carefully toss the doughnut in the sugar mix until coated. Place back on the wire rack.
Donuts keep well at room temperature in a semi-airtight container for 2-3 days (I store them in a glass cookie jar.)