In a large bowl either using a handheld or stand mixer fitted with the paddle attachment, beat the vegan butter for about 1 minute until creamy and smooth. Add the sugar and beat on high speed for 2-3 minutes until fluffy and light.
Now add in the almond milk, cornstarch, vanilla and almond extract (if using). Beat on high until it is all fully combined, about 1 minute. Scrape the sides of the bowl as needed.
Add 1 cup of the flour to the wet mixture. Sprinkle the baking powder and salt on top of the flour. Mix on low speed, until just combined. Now add 1 more cup of the flour and continue to mix on low until just combined; don't over mix. The dough should feel similar to play dough when you work it in your hands, but it will look crumbly in the bowl. If it seems too wet for rolling, add another 1/4 cup of flour. You want the dough to be thick, but not dry. I always use the full 2 1/4 cups of flour. If the dough is too wet, your cookies will spread.
Using a spatula, scoop all of the dough out of the bowl; use your hands if needed to push it all together. Divide the dough in half and roll into two balls.
On a flat surface, add a sheet of parchment paper. Sprinkle a little flour on it, then add half the dough. Sprinkle a little flour on top of the dough, and roll it out to about 1/4 inch thickness. Place a sheet of parchment paper on top. Repeat for the second ball of dough, and then stack them with parchment paper. Chill in the refrigerator for at least 1 hour or overnight.
Once the dough has been chilled, set it on the counter for 10 minutes while the oven is preheating to 350 degrees F. Line two baking sheets with parchment paper. Cut into desired shapes using a cookie cutter and place them on the prepared baking sheets. Continue re-rolling the dough until it is all used.
Bake for 8-10 minutes, in the middle rack of the oven, until very lightly colored on top and around the edges. They will appear underdone, but they will firm up considerably as they cool. Let them cool for 5 minutes, and then transfer to a wire rack to let cool completely before icing.