Preheat oven to 350 °F.
In a bowl, stir the dry ingredients (rice flour, tapioca and potato starches, baking powder, salt and xanthan gum) together.
In a separate bowl, cream shortening and sugar together until fluffy. Scrape down sides. Mix together oil, baking powder and water. This is your egg substitute. Add egg substitute and vanilla, and continue beating. Add flour mix slowly and stir (LOW speed) until completely combined.
Dough will be very wet/sticky–it will remind you of cake frosting. Add potato starch, 1-2 Tbsp at a time, until dough is thick enough to turn out onto counter dusted with potato starch. (Though it will stick mostly to itself and not your fingers, you will have to use spatula to get dregs out of bowl.) Begin kneading dough, adding potato starch as needed until dough is thick/dry enough to roll out.
Add food color now, if desired. Just knead in until dough is uniform in color. If it’s not enough color, knead in more. No gluten means you can’t overwork dough.
Roll out dough to 1/4 inch thick, and cut cookies. Place on greased or parchment lined cookie sheets. Bake for 15-17 minutes. Remove from oven and cool slightly on pan before transferring to wire rack.
If not avoiding egg, the egg replacer mixture (oil/baking powder/water) can be replaced with 1 egg.