Drop the tablespoons of coconut oil and vegan butter onto a small plate lined with parchment paper, flatten slightly and place in the freezer for about 10 minutes.
Combine apple cider vinegar and cashew milk (or other preferred non-dairy milk) to make vegan "buttermilk". Set aside.
In a large mixing bowl, combine the flours, baking powder, baking soda and salt. Mix well with a whisk until thoroughly combined.
Take the fats out of the freezer and, working quickly, chop them as finely as you can with a sharp chef knife. If after you're done you find that the chopping action has made the fats soft again, return them to the freezer for a few minutes.
Add the cold, finely chopped fats to the flour mixture and mix well with a wooden spoon or rubber spatula. Check the consistency of the mixture with your fingertips; it should feel like coarse sand. If you find the odd larger chunk of fat, simply break it down with your fingers.
Make a little well in the center of the mixture and pour in the cold "buttermilk". Stir delicately until the dough just barely comes together; it will be very sticky.
Turn the dough onto a floured work surface, dust the top with a little bit of flour and gently shape it into a flat ball. Then, using your fingers (not a rolling pin) flatten that ball of dough into a 3/4" thick round, rotating often to ensure the dough isn’t sticking. For taller biscuits, you can shape the dough to 1" thickness instead, but you'll get fewer biscuits.
Cut out your biscuits with a 2-1/4" round cookie cutter. Be sure to push straight down through the dough without twisting, as doing so might prevent the biscuits from rising.
Arrange the biscuits on a baking sheet so that they touch but just barely; this will help them rise evenly.
Gently reshape the leftover dough into 2-3 more biscuits, working the dough as little as possible. (biscuits from leftover dough will not be quite as puffy as those from first pass, but they'll still be very yummy!)
Brush the tops with a little bit of melted vegan butter or olive oil and bake for 12 to 15 minutes, or until the biscuits puff and turn slightly golden brown.
Serve without delay.
Any leftover biscuits will need to cool completely before you can store them, at room temperature in an airtight container.