Preheat your oven to 350°F. Line a baking sheet with parchment paper and set aside.
Make the flax egg by stirring together the ground flaxseed and water in a small bowl. Let it sit for about 5 minutes until thick and gel-like.
Place the softened vegan butter and granulated sugar in a large mixing bowl. Beat with a hand mixer (or sturdy spoon) for 2–3 minutes until the mixture looks lighter in color and fluffy in texture.
Add the prepared flax egg and vanilla extract to the butter mixture. Mix again until fully incorporated and smooth, scraping down the sides of the bowl as needed.
In a separate bowl, whisk together the flour, cream of tartar, and baking soda so the leavening is evenly distributed.
Add the dry ingredients to the wet ingredients. Mix on low speed or by hand just until a soft dough forms and no dry flour patches remain. Do not overmix — stop as soon as combined.
Scoop tablespoon-sized portions of dough and roll each into a smooth ball using your hands.
Pour the sanding sugar into a small bowl. Roll each dough ball in the sanding sugar until fully coated on all sides.
Place the coated dough balls on the prepared baking sheet, spacing them about 2–3 inches apart to allow for spreading.
Bake for about 11 minutes. The cookies should have set edges, light surface cracks, and soft-looking centers.
Let the cookies cool on the baking sheet for 5 minutes, then transfer to a rack to cool completely. They will firm up slightly as they set.