Preheat the oven to 350 degrees F and line two baking sheets with parchment paper. In a large bowl, add the sugar and canola oil. Stir until well combined and smooth.
Add the ground flax seeds, non-dairy milk, and vanilla. Mix well to combine.
Sift together the flour, cocoa powder, baking powder, and salt using either a sifter or fine mesh strainer. Fold in with the wet ingredients until a soft dough is formed.
Place the powdered sugar in a small mixing bowl. Scoop out a heaping tablespoon of dough at a time, and shape it into a ball.
Roll the ball in the powdered sugar very generously, covering all sides. The more powdered sugar, the prettier the cookies will be.
Place the balls onto the prepared baking sheet, about 2 inches apart so they have room to spread.
Bake for 10-12 minutes until set. They will appear slightly undercooked and soft but will firm up as they cool.