Heat a frying pan over medium heat.
Add 1 tablespoon of vegetable oil to the pan and add in the red bell pepper, green onion and chopped turkey slices.
Sauté for about 1-2 minutes, until the ingredients are warmed through.
Remove from heat.
Add in 2 tablespoon of BBQ sauce to the turkey mixture and stir with a spoon to coat evenly.
Warm a large 8" flour tortilla in the microwave (about 20 seconds).
Add a handful of cheese to the bottom half of the tortilla.
Top with half of the turkey mixture.
Add about 2 tablespoon of caramelized onion jam.
Add another handful of cheese on top of the onion jam and fold the tortilla in half. Press firmly to close.
Repeat with the remaining tortilla.
Heat the BBQ to 350°F/177°C.
Add the quesadillas to the grill and cook for about 2-3 minutes per side, until cheese melts.
Remove quesadillas from the grill.
Cut quesadillas into wedges with a sharp knife and serve.