In a large bowl using a 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.

Add in the plant milk, cornstarch, and vanilla. Beat on high until combined, about 1 minute. Scrape the sides of the bowl as needed.

Add 1 cup of flour to the wet mixture. Add the baking powder and salt. Mix on low speed, until combined. Add 1 more cup of the flour and continue to mix on low until just combined; do not 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 ¼ cup of flour. You want the dough to be thick, but not dry. If the dough is too wet, your cookies will spread.

Scoop all of the dough out of the bowl; use your hands to push it all together. Divide the dough into two balls.

Chill in the refrigerator for at least 1 hour or overnight.

Once chilled, allow to warm to room temperature. Roll dough to ¼ inch sheet and 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 will firm up considerably as they cool. Let them cool for 5 minutes, and then transfer them to a wire rack to cool completely before icing.

Whisk all icing ingredients in a bowl. If it seems too thick, add a little more plant milk. It should be smooth, glossy, and not runny. If too runny, add more powdered sugar.