Combine the shredded chicken and 3 teaspoons of the taco seasoning in a bowl. Stir until chicken is well coated. (I like to heat the chicken in a skillet or the microwave, but that step is optional.)
Heat a large large non stick skillet over medium heat. Add the oil and onion and saute for 3-4 minutes.
Add the peppers and remaining 2 teaspoons of taco seasoning and saute for another 3-4 minutes. Set aside.
Wipe out the skillet and heat to medium low. Spread 1/2 teaspoon of butter on a tortilla. Place butter side down in the warm skillet.
On half of the tortilla, sprinkle 1/4 cup of the cheese, 1/2 cup of the chicken, 3-4 tablespoons of veggies, and some diced jalapeno if desired. Top with anther 1/2 cup cheese.
Fold the tortilla over and cook for 2-4 minutes, or until golden brown and cheese starts to melt. I like to add a lid so the steam helps the cheese melt.
Carefully flip to the other side and cook for another 2-4 minutes or until cheese is melting out and tortilla is golden brown. Repeat for remaining tortillas.
Cut into wedges and serve hot.
Notes
For a spicier quesadilla, don't remove the seeds from the jalapeno.
Heating the chicken will help the cheese on the inside melt faster.
I will sometimes use my electric skillet and cook 2 quesadillas at once.