Step 1: Prepare the Dough
In a small bowl, combine warm milk and pinch of sugar. Sprinkle the yeast over the top and let it sit for 5-10 minutes until it becomes foamy.
In the bowl of a stand mixer with a dough hook, mix together the warm milk, sugar, eggs, softened butter, and vanilla extract until smooth.
In a separate bowl, whisk together the whole wheat flour, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined. The dough will be slightly sticky but should hold its shape. Turn the mixer on medium and knead for about 5 minutes until the dough comes together. At this point it should be slightly sticky and peeling of the bottom and sides of the mixer bowl. If it's too dry, add a little warm water (1 tablespoon at a time) until you reach a dough that is smooth but not too wet. Likewise, if the dough is too wet, add a tablespoon of flour at a time until it comes together and has a slight stickiness.Then, place the dough in a greased bowl.
Cover the dough with a damp tea towel or plastic wrap and let it rest at room temperature for at least an hour, or until it has doubled in size.
Step 2: Shape the Donuts
Once the dough rises, place dough on a lightly floured work surface and roll the dough to about ½-inch thick. If the dough is too sticky, sprinkle some flour on top.
Use a donut cutter or two round cookie cutters (one large, one small) to cut out the donuts and donut holes, and place on a piece of parchment paper. Keep a good distance between donuts so that they don't expand into each other. Place a damp towel over them.
Let the shaped dough rest for 1 hour in a warm place.
Step 3: Cook the Donuts
Fill a deep fryer, large pot, or dutch oven about 2-3 inches deep with coconut oil.
Preheat the coconut oil in to 350°F. (For best results see TIPS.)
Gently lower the donuts into the hot oil, cooking for 1-2 minutes per side until golden brown. Use a slotted spoon to remove them from the oil and place them on a paper towel-lined plate to drain.
Step 4: Glaze
In a small bowl, whisk together the powdered sugar, milk, and vanilla extract until smooth. Add more milk or sugar to adjust the thickness if needed.
Once the donuts are slightly cooled, dip the cooked donuts into the glaze, flipping them over so that the glaze coats both sides, allowing excess to drip off.
Step 5: Serve
Let the donuts rest for a few minutes to allow the glaze to set, then enjoy! These donuts are best served fresh but can be stored in an airtight container for a couple of days.