Preheat oven to 375°F (190°C) and lightly grease a 9x13 inch baking dish.
In a large mixing bowl, combine the shredded chicken, 1 cup of shredded Monterey Jack cheese, sour cream, and green chiles until well incorporated.
In a high-speed blender, combine the avocados, cilantro, lime juice, chicken broth, garlic, and salt. Process until a smooth, pourable sauce consistency is achieved.
Warm the corn tortillas in a microwave or dry skillet for 15 seconds until pliable to prevent cracking.
Place approximately 1/3 cup of the chicken filling into each tortilla, roll tightly, and place seam-side down in the prepared baking dish.
Pour the avocado cilantro sauce evenly over the assembled enchiladas, ensuring all edges are covered to prevent drying.
Top with the remaining 1 cup of Monterey Jack cheese.
Bake for 20 to 25 minutes until the cheese is melted and bubbling at the edges.
Let rest for 5 minutes to set before serving.