Preheat. Turn on the grill and preheat it to 400 degrees F.
Season. Season the chicken breasts on both sides with Fiesta seasoning.
Grill. Place the seasoned chicken breasts directly on the grill grates. Close the lid and grill the chicken breasts for about 6-8 minutes per side, or until the chicken reaches a temperature of 165 degrees F.
Rest and chop. Remove the BBQ chicken from the grill and rest for 10 minutes before chopping it into small cubes.
Make the sauce. While the chicken rests, prepare the avocado chipotle sauce. Add all ingredients to a blender jar and pulse until smooth. Refrigerate until ready to serve.
Assemble your quesadillas. Lay out 4 tortilla shells. Top each with a portion of quesadilla cheese and chopped chicken. Add another layer of cheese and top with a second tortilla.
Grill the quesadillas. Carefully transfer your tortillas to your hot grill. Cover with a lid and cook for 1-2 minutes, or until the cheese begins to melt. Use a metal spatula to flip the quesadillas. Close the lid and continue cooking for 1-2 minutes, or until the tortillas are cooked through and the cheese is melted.
Serve. Remove to a cutting board, slice into wedges, and serve with the avocado sauce and additional toppings, as desired.