Combine flour, salt, cream of tartar and baking soda in a mixing bowl. Add oil and water and mix with a wooden spoon or your hands until a stiff dough forms. If dough is sticky, use a bit more flour. If the dough is crumbly, add a bit more olive oil.
Divide dough in half, then in half again to create 8 fairly equal portions. Form each piece into a ball.
Place one dough ball at a time on a silicone baker’s mat, parchment paper or wax paper and flatten with the palm of your hand as much as possible. Cover flattened dough with a sheet of parchment paper or wax paper. Roll dough into a very flat rough circle, about 8-10 inches in diameter. Carefully remove the bottomsilicone mat or parchment paper, so the rolled-out tortilla is stuck to one piece of parchment paper or wax paper. Set aside and roll out the remaining dough balls (when they’re stuck to parchment or wax paper, you can easily stack them in preparation for cooking).
When pan is hot, peel one rolled-out raw tortilla off its parchment or wax paper and place into pan. Cook about 1 minute or until bottom surface has a few pale brown spots. The top surface will begin to show a few little bubbles. Flip and cook for about 30-45 seconds. [Ideally, the tortillas will be soft with a few small pale golden brown spots on surface. If tortilla is browning too fast, reduced heat a bit. If it’s taking longer than a minute to see a few pale golden brown spots on underside of tortillas, increase heat a bit.] Remove from pan with tongs and stack in a covered container until all tortillas are cooked.
Serve warm or allow to cool for later use. Store in an airtight container or resealable plastic bag at at room temperature for 24 hours or can be frozen indefinitely. To freeze, separate tortillas with parchment paper or waxed paper and place in a zippered bag before placing in freezer.