Heat a skillet over medium heat and add 1 tbsp oil. Add the chicken pieces and sprinkle with 1 tbsp taco seasoning. Cook for 4 minutes, stirring occasionally to ensure even cooking.

Add diced bell pepper and onion to the skillet with the chicken. Cook for an additional 5 minutes, or until the chicken is fully cooked and the vegetables have softened and gained some color. Remove the mixture from the skillet and set aside.

Wipe the skillet clean if needed, then add a small amount of butter or oil and heat over medium heat. Place one tortilla flat on the skillet surface.

Sprinkle some Mexican cheese on one half of the tortilla, then add a portion of the chicken and vegetable mixture on top of the cheese. Add more cheese over the filling to help everything stick together, then fold the tortilla over to create a half-moon shape.

Cook the folded tortilla for a few minutes until its underside turns golden brown and crispy. Carefully flip it over and cook the other side until golden and cheese inside melts. Repeat the process with the remaining tortillas and filling.

Remove quesadillas from the skillet and serve immediately while warm and gooey for best flavor and texture.