In a large skillet over medium heat, add 1 tablespoon of butter or oil. Add the thinly sliced onion and bell pepper. Sauté for 4-5 minutes until softened and slightly charred. Remove from heat and set aside.

In a mixing bowl, combine the 2 cups of cooked, shredded chicken with 2 teaspoons of taco seasoning. Mix well to coat the chicken evenly.

Wipe out the skillet and return it to medium heat with another tablespoon of butter. Place one flour tortilla in the pan. Sprinkle half of the tortilla with 1/2 cup of the shredded cheese. Top with 1/2 cup of the seasoned chicken and a portion of the sautéed vegetables. Sprinkle another 1/4 cup of cheese on top. Fold the empty half over the filling.

Cook for 2-3 minutes per side until the tortilla is golden brown and crispy, and the cheese is melted. Repeat with remaining ingredients to make 4 quesadillas total.

Transfer each quesadilla to a cutting board and let rest for 1 minute. Cut into wedges and serve immediately.