Add the cheetos to a large ziplocking bag. Using a rolling pin, crush them until all are finely ground. Set aside.
To a mixing bowl add the flour, half the ground cheetos, cream of tartar, baking soda, and salt. Whisk together until evenly combined.
Add the softened butter and sugar to the bowl of a stand mixture fitted with the beater attachment. Cream together until and the mixture's whipped and fluffy.
Crack the egg into the bowl, and add the drop of orange food coloring (if using). Mix together until smooth & creamy.
Add the dry ingredients, a little at a time, mixing together until they've all been incorporated and the batter's smooth. Set aside.
Pour the remaining ground cheetos out onto a large, shallow plate.
Scoop about a tablespoon's worth of dough out of the mixing bowl, and roll it into a ball. Roll the ball in the cheetos crumbs until evenly coated, then transfer to a waiting plate. Repeat until all the cookie dough's been used.
Lightly cover the plate with cling wrap (don't squish the dough balls!), and refrigerate for 2 hours or up to 8 hours.
When ready to make, transfer the balls to a parchment paper lined baking sheet and arrange them on the pan about 2 inches apart. You can bake in more than one batch, so don't overcrowd the pan.
Bake the cookies at 350° for 8-10 minutes. Remove from the oven, and allow them to rest for 5-10 minutes.
Transfer the cookies to a wire rack to finish cooling.
You can enjoy them warm, or wait until cooled completely to transfer them to an airtight container.