Heat your oven to 350°F. Spray a donut pan with vegetable spray.
In a small bowl, combine the ground flax seeds and water. Stir. Set aside.
In a separate small microwave-safe bowl add the vegan butter. Heat in a microwave until melted, around 20 seconds. Set aside.
In another small bowl, combine the flour, baking powder, baking soda, and nutmeg. Stir to combine.
In your mixing bowl add the sugar, vanilla plant-based milk, apple cider vinegar, flax egg mixture, and melted vegan butter. Stir to combine.
Roughly chop the blackberries. You want plenty of blackberries pieces to be present throughout the donuts.
Pour flour mixture over the liquid mixture. Drop blackberry pieces over flour and gently stir until the blackberry pieces are coated. Then start incorporating the flour into the liquid mixture. Stir until combined. Add purple food coloring if using.
Use a spoon to evenly distribute batter in each donut compartment, filling each to the top. This batter should fill up 6 compartments.
Bake 10 to 15 minutes, until the donuts are done and slightly golden colored on the top.
Remove from the oven and allow to cool for a couple minutes.
Make the Blackberry Glaze by combining the powdered sugar and coconut oil in a bowl. Stir to combine. It will be a dry mixture. Finely chop the blackberries and add them (along with as much of the juice as you can) to the glaze mixture. Stir to combine. Add the plant-based milk, one teaspoon at a time until you reach the desired consistency.
Coat each donut with the Blackberry Glaze. Serve warm.
* If you don't have vanilla-flavored plant-based milk, simply add a teaspoon of vanilla to regular plant-based milk **If you don't have purple food coloring, you can use 1 drop of red and 1 drop of blue food coloring