Get a medium campfire going, or get your charcoal on the go. (If you’re making this on a stove, use medium high heat and a nonstick pan.)
Add the chopped peppers, onions, and olive oil to a large cast iron skillet, and set over the fire or hot coals.
Cook until the veggies are tender, 5 minutes or so.
Add the chicken, chicken broth (or water!), paprika, garlic powder, and cumin to the pan, stir well, the season with a little salt and pepper.
Allow mixture to simmer for a couple of minutes, until most of the water has cooked off. Remove from heat.
Arrange tortillas on a clean work surface, or 4 large plates.
Divide half of the cheese among the tortillas, spreading it to cover half the surface of each tortilla.
Divide the chicken and pepper mixture among the tortillas, scattering it on top of the cheese layer only. Finally, divide the remaining cheese among the quesadillas, scattering it over the filling layer of each.
Fold the up-topped half of the tortilla over the fillings, and press down.
You can cook the chicken quesadillas in a pan, or directly on the grill grates.