1. Preheat the oven to 350°F. Lightly grease eight wells from two doughnut pans.
2. Mix the flaxmeal and water together in a small bowl and set aside.
3. In a medium bowl, combine the dry ingredients.
4. Add the applesauce, cider, oil, and vanilla, and stir to combine.
5. Combine all the wet and dry ingredients and stir.
6. Carefully divide the batter between the eight doughnut wells.
7. Bake for 10 to 12 minutes, or until the doughnuts have puffed up and the tops are golden brown.
8. Remove from the oven and after a few minutes, place the doughnuts on a cooling rack.
9. While they're cooling, mix together the icing ingredients in a small bowl.
10. Once the doughnuts are completely cooled, drizzle with icing and enjoy!

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