In a large bowl, toss together the chicken with 1/2 teaspoon of the salt and the remaining spices, until evenly combined.
In a large skillet, heat about 1 tablespoon of oil over medium high heat. Add the seasoned chicken and cook, stirring occasionally, until chicken is cooked through, about 6 minutes. Remove chicken to a clean bowl.
In the same skillet, add the peppers and onions and cook until softened and slightly browned. Add in the garlic and cook for another 30 seconds. Add to the bowl with the chicken. Add the 2 tablespoons of minced chipotle peppers, 1 tablespoon of adobo sauce and the chopped cilantro. Mix until combined.
In a small bowl, mix together the Greek yogurt, juice of half a lime, ½ teaspoon of salt and remaining 1 tablespoon of the adobo sauce. Set aside.
Heat a large skillet over medium low heat. Evenly sprinkle ¼ cup of the shredded cheese on the bottom half of each tortilla. Evenly spread over ¼ of the chicken and pepper mixture on top of the cheese then top with another ¼ cup of the cheese. Then fold the top half over.
Add a small amount of oil to your hot skillet. Gently place your quesadilla in the pan and cook for 3-4 minutes per side, until the outside is crispy and the cheese is melted. Remove to a cutting board and let rest for 2 minutes. Cut into thirds and serve with extra chopped cilantro and the chipotle Greek yogurt sauce.