First, make the flax egg by adding the ground flax and water to a small bowl. Mix together and set aside for 5 minutes until thick and gelatinous.
Add the vegan butter and ½ cup sugar to a mixer and cream together until light and fluffy, about 1-2 minutes. Then, add in the flax egg and vanilla. Mix all the wet ingredients together for around 30 seconds.
Add the all-purpose flour, baking powder, and salt to the mixing bowl. Mix into a thick cookie dough. Then, use a spatula to gently mix/fold in the rainbow sprinkles.
Add the bowl of dough to the fridge, cover, and let chill for 30 minutes.
Once the dough has chilled, remove it from the fridge. Preheat the oven to 350F and line a baking sheet with parchment paper.
Use a 1.5 tablespoon cookie scoop to scoop our 8 cookie dough balls. Roll each cookie dough ball between your palms to form a round ball. Then, roll each ball in a bowl with the remaining 2 Tablespoons of sugar that was set aside so that each dough ball is coated in sugar.
Place the cookie dough balls on the parchment-lined baking sheet, making sure to keep them 1-2 inches apart so they have room to spread while baking.
Then, bake for 12-14 minutes until the bottoms are lightly browned and the cookie is cooked through but has slightly soft centers. The cookies will continue baking after they are removed from the oven so the centers should still be soft, but not glossy or raw, when they are removed from the oven. If you would like to make smaller cookies (about 10 vs. 8) make sure to adjust the baking time to 11-13 minutes.
Once you remove the tray of cookies, lightly tap it on the counter to produce a more "wrinkly" cookie. You can also swirl them inside a large mug or biscuit cutter for a rounder cookie.
Let the cookies cool on the baking sheet for 5 minutes. Then, transfer to a wire rack to continue cooling.
Once the cookies have cooled, serve and enjoy!