In a large skillet over medium heat, swirl the olive oil to coat the pan. Add the peppers and onion and cook until soft, about 5 minutes. Add the chopped chicken and heat through. Add the seasoning, water, spaces, and marinade and stir to coat. Lower heat to a simmer and mix until all liquid is almost absorbed.
Meanwhile, preheat panani press, grill, or another skillet to make the quesadillas in. Spray the surface with a quick burst of cooking spray and lay a tortilla on in. Spoon in chicken mixture and top with cheese and another tortilla. Press. Cook until tortilla is golden brown and cheese is melted, flipping if needed (if using a panini press don't flip. That would be silly.)
Carefully transfer to a cutting board and, using a pizza cutter, slice and serve with desired fixings.