Heat oil in a 12 inch skillet. Add steak and heat until just heated through. Toss in the spinach and cook until wilted. Remove steak and spinach from the pan. Place one tortilla in the pan and heat through. Flip the tortilla and place half a slice of cheese on one half of the tortilla.
Layer the steak and the spinach over the cheese and then place another half slice of cheese on top. Fold the tortilla onto itself to create a half moon. Place a tea kettle or another heavy pot on top of the tortilla to press it down for about 30 seconds. Flip the quesadilla and do the same thing on the other side.
Remove quesadilla from the pan and allow to cool bait before slicing in half. Enjoy with some plain Greek yogurt and spicy garlic sauce.