In the bowl of a stand mixer on medium speed (or using a hand mixer)beat together the sugars, vegan butter, almond milk, and vanilla extract.
Beat in the remaining ingredients until just combined. Cover and let the cookie dough sit in the fridge for at least 2 hours or even overnight.
When ready to bake, pre-heat to oven to 375 degrees F and line 2 baking sheets with parchment paper or a silicon mat.
Generously flour your working surface as well as your rolling pin and cookie cutters. If the dough seems a bit sticky on the outside, gently pat it with a little flour and continue to do so while you roll it out if sticky areas are exposed.
Working in about 2 sections, roll the dough out to about 1/4 in thickness and cut out your cookie shapes and place them on your baking trays. Leave about an inch and a half between each cookie.
Repeat until all of the dough is used. (side note: I baked the cookies in 2 batches and end up with 4-5 baking trays of cookies. This depends on the size of your baking trays.
Bake for 7-8 minutes, taking the cookies out of the oven just when the edges begin to brown. Put the cookies on a cooling rack and let cool before putting icing on.