Preheat oven to 350ºF. Line several baking trays with parchment paper. Mix together the flour, salt and baking powder. Set aside.

Blend together (in a stand mixer or food processor, or with a hand blender) the vegan butter, powdered sugar, non-dairy milk and vanilla. Add in the flour. Dough should appear somewhat dry, but should stick together when pinched together with your fingers. If the dough seems too dry and a little more non-dairy milk. Do not add too much liquid.

Empty dough from mixer or processor onto a lightly floured surface. Take a large handful and, in your hands, press together to form a ball, then flatten the ball on the floured surface. Using a rolling pin, roll the dough to a thickness of about 1/8 inch, the cookies will puff a little when you bake them. Using a cookie cutter or a glass, cut cookies and place them on prepared baking tray. Bake for 12 to 15 minutes. Remove from oven and sift powdered sugar over them. Re-roll scraps and repeat process until all the dough is gone.