01 - Set oven to 375°F (190°C). Lightly grease a 9x13-inch baking dish with nonstick spray or butter.
02 - In a large mixing bowl, combine shredded rotisserie chicken, 1 cup Monterey Jack cheese, 1/2 cup sour cream, softened cream cheese, sliced green onions, 1/4 cup green chiles, ground cumin, garlic powder, salt, and black pepper. Mix thoroughly until well blended.
03 - In a medium saucepan over medium heat, melt butter. Stir in flour and cook for about 1 minute, whisking constantly to form a smooth paste.
04 - Gradually whisk in chicken broth until no lumps remain. Continue cooking and whisking until thickened, approximately 3 to 4 minutes. Reduce heat to low, then add 1 cup sour cream, 1/2 cup Monterey Jack cheese, and 1/4 cup green chiles. Season with salt and black pepper to taste. Stir until cheese is melted and sauce is creamy. Remove from heat.
05 - Place a generous scoop of chicken filling across the center of each flour tortilla. Roll each tortilla tightly and arrange seam-side down in the prepared baking dish.
06 - Evenly pour white sauce over arranged enchiladas. Sprinkle remaining 1/2 cup Monterey Jack cheese on top. Bake in the preheated oven for 20 to 25 minutes, until heated through and cheese is melted and bubbly.
07 - Remove from oven. Garnish with freshly chopped cilantro, if desired. Serve hot.