Prepare grill on high heat, and have all ingredients ready and chopped. Mix together both cheeses in a bowl.
On one half of tortilla sprinkle half of cheese mixture, then all of your meat and vegetables. Top with the rest of the cheese and fold over, pressing down to hold together. Brush sides of quesadilla with oil, place on hot grill, flipping over when one side is nice and brown.
Make sure to cover grill in between so cheese melts.