For the quesadilla seasoning, mix all ingredients in a small bowl.
Season the chicken with 1 tablespoon of the quesadilla seasoning. You can do this step up to a few hours ahead and refrigerate the chicken until ready to use.
Heat the olive oil in a large skillet on medium-low to medium heat. Add the peppers, onions, and ¼ teaspoon salt and sautée, stirring occasionally, until soft and golden brown, about 10-15 minutes.
Add the seasoned chicken, red pepper flakes, and the remaining ¼ teaspoon salt and cook, stirring occasionally, until the chicken is fully cooked, about 5 minutes. Remove the pan from the heat.
Lightly brush one side of each flour tortilla with olive oil. On one of the non-oiled sides, place ½ cup of shredded cheese. Top it with ¼ or ½ of the chicken mixture (¼ will yield thinner quesadillas, ½ will yield thicker ones), then top the chicken with another ½ cup shredded cheese.Repeat the above with the second flour tortilla.
Take the two remaining flour tortillas and place them oil-side up on top of the tortillas with the filling. Heat up a flat panini maker (no ridges), griddle pan, or standard pan large enough to hold at least one quesadilla. When it's hot, place the quesadilla on it.
If using a panini maker, cook until both sides are golden brown and the cheese is fully melted. If using a griddle or standard pan, flip the quesadilla carefully over once the underside is golden brown and crispy.
Repeat the process with the second quesadilla. Slice each quesadilla into quarters and serve alongside whatever you like. Enjoy!
Notes
Note 1: Make sure to cut away the tendon (the little white strips) from each tenderloin as you slice the chicken. It's safe to eat, but its chewy texture may be unpleasant.Note 2: You can purchase a block of cheese and grate it yourself or buy it pre-shredded.