Add all the ingredients for the chicken to a large bowl and toss together to coat. Cover with plastic wrap and set aside while you cook the vegetables.
Make the peppers and onions. Heat the olive oil in a large skillet over medium-high heat. Add the peppers, onions, soy sauce, and kosher salt. Cook for 10 minutes, stirring occasionally, until the onions are translucent and begin to caramelize and the bell peppers are soft and tender. Transfer them to a bowl and cover with foil or plastic wrap to keep warm.
To the same hot skillet, add 1 teaspoon of olive oil and the seasoned chicken. Cook for 10 minutes, flipping halfway through, until the chicken reaches an internal temperature of 165℉ and is fully cooked through.
Remove the pan from the heat and transfer the chicken to a cutting board and let it cool slightly before chopping into bite-size pieces.
Add the diced chicken, peppers, and onions back to the skillet, and give it a quick toss to combine. Set aside.
Working in batches of 2, melt 1 tablespoon of butter in a large skillet over medium-high heat.
Layer half of each tortilla with ¼ cup shredded cheese, ½ cup chicken fajita mixture, and another ¼ cup shredded cheese. Fold it over and cook the quesadillas in the skillet for 1 to 2 minutes per side until the cheese has fully melted and the quesadillas are golden brown. Repeat with the remaining quesadillas and butter.
Serve with guacamole, sour cream, and your favorite salsa.
Notes
Choose the right tortillas. Opt for large 10-inch flour tortillas (sometimes called "burrito size") for flexibility and ease of folding. If you're aiming for a more authentic taste or a gluten-free option, corn tortillas are a great alternative. However keep in mind they're often smaller, so you'll need to adjust the amount of filling and cheese accordingly.
Don't skip the butter. This helps toast up the outside of the tortilla and get it crispy and golden brown. It makes a huge difference in the taste!
Use a good melting cheese. Choose a cheese that melts well, such as Chihuahua, Monterey Jack, Cheddar, or Oaxaca. These cheeses will give your quesadillas the perfect gooey texture.