In a small bowl, whisk together the yeast and milk and set aside until foamy, about 5 minutes.

In a blender, blend up the water and flax for about a minute until frothy and viscous, kind of like an egg white. Set aside.

In a very large mixing bowl, whisk together the flour, sugar, and salt, then make a well in the center. Pour in the yeast mixture, the flax mixture, and the coconut oil, then mix to form a dough. Add more flour a tablespoon at a time until the dough is soft and slightly tacky, but not dry. Then turn it out onto a floured counter to knead until the dough is smooth and elastic, about 8 minutes.

Wash out the mixing bowl, lightly coat it with nonstick cooking spray, and add the dough ball. Toss the dough ball to coat it in oil, then cover the bowl with plastic wrap. Place the bowl somewhere warm and let the dough rise until doubled in size, 1 to 2 hours.

Lightly flour the counter and a baking sheet. Turn out the dough onto the floured counter, knead it a couple of times, then roll it out until it’s about ½ inch thick. Using a floured 3-inch cookie cutter (or a drinking glass), stamp out your doughnuts and place them on the floured baking sheet at least 2 inches apart. Dip the cutter in flour between cuts to prevent sticking. Squish the dough scraps back together and roll them out again to make more doughnuts, then cover the sheet with a clean kitchen towel or plastic wrap and let the doughnuts rise for about 20 minutes.

While the doughnuts are rising, get your fryer ready (see instructions above) and preheated to 350°F. Have ready a layer of paper towels or brown paper bags to drain. Pour some sugar into a shallow dish for coating the doughnuts.

Using a metal slotted spoon, lower the doughnuts into the oil, a few at a time so you don’t crowd the fryer, and fry until golden brown, about a minute and a half on each side. Use the slotted spoon to transfer them to the paper towels or bags until cool enough to handle but still warm, then roll each one in sugar until completely covered.

Once all the doughnuts are fried and sugared, it’s time to fill them! Fit a pastry bag with a large round tip and fill it with the jam. Poke the tip into the side of each doughnut, wiggling gently to create a little space inside, then squeeze a nice blob of jam inside! If you overfill them, the jam will leak out, but that’s okay. Serve! Store any leftovers in a paper bag, if you can manage to not eat them all right away.