In a pan set over medium heat, sauté the onion, pepper, and chorizo in 30 ml (2 tbsp) of oil for 5 minutes.
Place 4 pita breads on a clean work surface. Top each pita with the two cheeses. Next, add the chorizo mixture, black olive tapenade, and parsley. Place a second pita bread over top and press down gently.
In a large non-stick pan set over low heat, toast one quesadilla at a time in 15 ml (1 tbsp) of oil, approximately 3 minutes each side.
Serve with the sour cream, tomato sauce, and oregano.