Cut chicken breast into strips or dice. Chop onion, slice green pepper, and mince garlic.
In a frying pan, use 2 teaspoons of oil to saute the chicken until browned and not longer pink inside. Remove from heat and set aside. Drain frying pan.
Add 2 more teaspoons oil to saute the chopped onion and peppers until soft. Add in chopped garlic and saute, adding salt, pepper, and taco seasoning. Remove from the heat once cooked and set aside.
Drain and rinse the black beans. Set aside.
In a clean frying pan, add one tortilla with one side oiled and place oil side down. Sprinkle wit 5 tablespoons of cheese. Add 1/5 of the cooked chicken, 1/5 of the black beans, 1/5 of the vegetable mix, and another 5 tablespoons of cheese. Top with a second tortilla.
Cook until bottom tortilla is lightly browned and the cheese has started to melt, then flip. When the second side is cooked the same, remove the quesadilla from the frying pan. Repeat with the remaining ingredients.
Cut the quesadillas into quarters and serve with soured cream.