In a small bowl stir to combine mayonnaise, mustard, and honey. Set aside.
Lay 4 of the tortillas on a countertop. Top each with 2 slices ham and apple slices, then divide cheese between them. Top with remaining 4 tortillas.
In a large nonstick skillet heat 2 teaspoons oil over medium heat. Cook 2 quesadillas at a time, turning once, until browned on both sides. Repeat with remaining 2 teaspoons oil and quesadillas.
To serve, cut quesadillas in half and serve with honey mustard.