Preheat oven to 350°F Lightly grease baking sheets.
Add oil, baking powder, sugar, soy milk, and extract to a mixing bowl and combine with a whisk.
Stir flour in 1/2 cup at a time with a large spoon. When the dough is too thick to mix any more flour in with the spoon, knead it in with your hands. NOTE: I use Silk soy milk. The wet/dry balance of the dough may vary depending on the type and even brand of milk substitute you are using. The dough should form a ball when squeezed together but not be sticky in your hands. As you add flour, knead each 1/2 cup addition in thoroughly and check for this. If it is getting too dry to hold together as a ball, either stop adding flour or add a bit more of your liquid. If it is sticky feeling, you need a little more flour.
When your dough is done, take a handful of dough, shape it into a ball in your hands, and roll the dough out on a floured surface. If the dough is sticking to the rolling pin, dust the top of the ball of dough with flour before rolling. (If after a while the dough becomes too dry to form a ball after repeated rolling out and dusting with flour, knead 2-3 drops of water into it to get it to form a ball again. ).
Cut into desired shapes. Lift shapes with spatula onto lightly greased baking sheets.
Bake for about eight minutes. Cookies are done when points are showing the slightest hint of brown, or just before that. Use a spatula to loosen cookies from sheets immediately.