Preheat your oven to 425 degrees F, and line a baking sheet with parchment paper.
In a large mixing bowl, whisk together the all-purpose flour, baking powder, baking soda, cane sugar, and salt.
Cube or grate the frozen butter into the flour mixture, then use a pastry blender or fork to incorporate it until the mixture resembles a coarse meal. Transfer the bowl to your fridge to chill for 10 minutes.
In the meantime, add soy milk and vinegar to a small bowl or container. Whisk them together, then set aside for 5-10 minutes to form the vegan buttermilk.
Remove the flour mixture from the fridge and add the vegan buttermilk. Stir with a spatula until just combined, being careful not to overmix.
Turn the dough out onto a floured surface and form it gently into a ball. Roll or pat the dough into a ½-inch thick rectangle.
Cut the dough in half with a pastry cutter, and stack the two pieces on top of one another. Gently re-roll the dough into a ½-inch thick rectangle. Cut the dough in half and stack it once more, then roll it to ¾-inch thick.
Cut the dough with a 2 ½ - 2 ¾-inch biscuit or cookie cutter, being careful not to twist the cutter.
Transfer the biscuits to the prepared baking pan, leaving some space in between each one. Re-roll the leftover dough and cut it again until it is all gone (you should end up with about 6-8 biscuits in total).
Brush the tops of the biscuits with extra soy milk, then bake them for 12-14 minutes, or until they are golden brown.
Once the biscuits are baked, transfer them to a wire rack to cool for a few minutes. Serve while warm. Happy eating!