Mix the flour, salt, and cream of tartar together in a 2 quart saucepan.
Add the water, oil, and peppermint extract to the flour mixture.
Turn on the burner to medium/low heat and stir.
Keep stirring until the mixture starts feeling a little more solid. You can tell when it starts separating a little at the bottom of the pan. This could take anywhere from 20 seconds to 2-3 minutes, depending on how hot your stove is.
Add the food coloring right away. The playdough begins to solidify quickly from here, so it’s easiest to mix the food coloring in just before that point.
Now dump the ball of playdough onto a plate or piece of waxed paper to cool. It won’t be super hot, but I usually let it cool for about 5 minutes before kneading it to get any lumps or food coloring mixed in completely.