In a medium or large bowl, mix together the cane sugar, 1 cup of the all purpose flour, instant yeast, oat milk, oil (I used avocado oil), applesauce, and vanilla. Cover with plastic wrap or a towel and rest for about 20 minutes. Add in the salt, flaxseed meal if using, the rest of the all purpose flour, and white whole wheat flour. Knead the dough with your hands for about 5 minutes and add extra flour as needed. Be very careful not to add too much or they will turn out dry.
Cover with plastic wrap or a towel and let it sit for an hour to 2 hours. It should double in size.
Lightly flour your surface and roll out the dough to be ¼ or ⅓ inch thick. Cut out using a donut cutter. If you don't have one, you can try using cups or cookie cutters. You can also use bottlecaps for the holes. Try to cut as much as you can before re-rolling, because you it will get dryer each time.
Line a baking tray with aluminum foil or parchment paper and lightly spread oil. Place the donuts on the tray, then cover and rise for about 20 minutes. Brush on more oil, then bake at 350 degrees Fahrenheit for about 7 minutes (depending on size and oven).
To make the glaze, pour powdered sugar in a shallow bowl, then add very small drips of oat milk. A little goes a long way! Keep mixing and adding milk until the icing is runny but not too thin. If it gets too thin, or you run out, you can always add more powdered sugar. Do not skip the glaze! It adds a lot of the flavor.
Once the donuts finish cooking, dip them in the glaze so they're coated on all sides. Let them drain on a cooling rack and harden. Enjoy!