Make the Green Chile White Sauce: Melt butter in a medium saucepan over medium heat. Whisk in flour and cook for 1-2 minutes until bubbling and golden. Gradually whisk in chicken broth until smooth. Bring to a gentle simmer and cook for 3-5 minutes until thickened.
Whisk in Sour Cream & Chiles: Remove saucepan from heat. Whisk in sour cream, diced green chiles, ground cumin, garlic powder, onion powder, salt, and pepper until velvety smooth. (Removing from heat prevents the sour cream from curdling.)
Prep Tortillas & Base: Preheat oven to 350°F (175°C). Spread 1/2 cup of the white sauce across the bottom of a 9x13-inch ceramic baking dish. Warm tortillas in microwave for 30 seconds wrapped in damp paper towels to make them pliable.
Fill & Roll: Down the center of each tortilla, place a generous spoonful of shredded chicken and a sprinkle of Monterey Jack cheese. Roll tightly and place seam-side down in the baking dish.
Sauce & Cheese Crown: Pour all remaining creamy white sauce evenly over the rolled enchiladas, coating every corner. Top generously with the remaining 1 1/2 cups of shredded Monterey Jack cheese.
Bake to Bubbly Perfection: Bake uncovered for 22 to 25 minutes until the sauce is vigorously bubbling around the edges and cheese is completely melted. Broil on high for 2-3 minutes for golden toasted cheese spots.
Garnish & Rest: Let rest for 5 minutes before serving so the sauce sets. Garnish with chopped fresh cilantro, diced avocado, and lime wedges.