Mix the mustard and honey together and spread over one of the tortillas. Lay the ham on top and sprinkle with the Cheddar. Sandwich with the second tortilla.
Preheat a large nonstick frying pan over medium heat. Slide in the assembled quesadilla, cheese side down, and cook for 1 to 2 minutes. Flip onto the other side and heat through for 1 minute more. Remove from the pan and let stand on a plate for 3 to 5 minutes before cutting, to stop the cheese from oozing out.