Mix together the rotisserie chicken, softened cream cheese, half of the green chilies, half of the Monterey jack cheese, and spices in a large bowl.
Place the seasoned rotisserie chicken and cheese mixture in the center of the tortilla shells and roll to create a cylinder with holes on each end.
Place the filled tortillas in a casserole dish with the seam side down.
In a saucepan, combine the chicken broth, heavy cream, sour cream, and the remainder of the green chilies. Bring it to a simmer and slowly add the remaining Monterey jack cheese, stirring frequently.
Pour the sauce over the filled tortillas in the casserole dish and bake at 375F for 10 minutes or until bubbly.