Preheat your griddle on medium-low heat.
Add a splash or two of oil and let it get hot.
Add the diced meats. Cook for 2 minutes, mixing the meats around to get a little char on them and release some of the juices.
Add the garlic and Italian dressing and seasoning. Stir and cook another 4-5 minutes until the garlic is cooked and the dressing is mostly cooked off.
Slide the meats off to the side of your griddle and keep warm. If you don't have room, you can remove them to a plate.
Add a splash or two more of the oil to the griddle.
Add the tortillas. Sprinkle half of the cheese and peppers on one half of each tortilla.
Top the cheese with the deli meat, putting half on each tortilla.
Fold over the non-topped, empty side of the tortilla to form a half-moon quesadilla.
Cook for 3 minutes then flip carefully (a long spatula helps) and cook another 3 minutes or until the cheese is melted and the tortilla is cooked until nice and golden brown.
Remove and let cool slightly before slicing and serving.