Remove the meat from the rotisserie chicken. This should yield around 12 ounces of chicken, give or take. Shred into small pieces.
In a large sauce pan, saute the onion and garlic over high heat for 2-3 minutes, until softened.
Stir in the salsa and sour cream. Then reserve 1 cup of the mixture, set aside.
To the pan, stir in the chicken, 1 cup cheddar, and 1 cup quesadilla cheese.
Add 1/4 cup of the reserved sauce to the bottom of a casserole pan.
Roll the filling into the tortillas, placing in the prepared pan. Top with the remaining sauce, 1/2 cup cheddar, and 1/2 cup quesadilla cheese.
Bake at 400°F for 15-18 minutes, until the cheese is bubbling.
Top with cilantro and cotija.