Combine all the ingredients under Chicken marinade in a large bowl. Mix well so that the chicken pieces are evenly coated. (You can cook the chicken right away, or set it aside to marinate for 30 minutes.)
In a hot pan with olive oil, add in the marinated chicken and cook for about 6-8 minutes, or until completely cooked. Keep stirring the chicken to ensure that it cooks evenly. Set the cooked chicken aside in a large bowl.
In the same pan, add olive oil and add in the chopped onion, green pepper, red pepper, green chilies, garlic and green onions. Sauté until the vegetables are slightly browned.
Season the vegetables with oregano, ground black pepper and salt and mix well. Once the vegetables are done cooking, add them to the same bowl as the cooked chicken and mix well. This is your quesadilla filling.
Heat the tortillas on a pan, but only on 1 side.Remove from heat and place the tortilla on a plate, cooked side up for assembly. Mix the ingredients under Spicy mayo and spread about 1 tbsp of it on each tortilla. Now add about ½ cup of the quesadilla filling on each tortilla. Sprinkle ¼ cup of shredded cheese over the filling. (See pictures above.) Fold the tortilla in half and spread a thin layer of butter on top. Place the buttered side down on a hot pan.
Flip the quesadilla once it becomes golden brown. Once both sides are done, transfer onto a cutting board and portion it like a pizza!
Serve with sour cream and lime wedges! Bon appétit!