Start by preheating your oven to 350°F and lightly grease a 9x13 inch baking dish. While the oven heats, combine the shredded rotisserie chicken, softened cream cheese, garlic powder, onion powder, and 1 cup of the monterey jack cheese in a large mixing bowl. Stir until everything is well combined and the cream cheese is evenly distributed throughout—the mixture should be creamy and cohesive. This is your filling base, and doing this first ensures it's ready when you need to assemble the enchiladas.
Melt the butter in a medium saucepan over medium heat. Once melted, sprinkle the flour over it and whisk continuously for about 1-2 minutes to create a light roux—this removes the raw flour taste and helps thicken the sauce. Add the taco seasoning and whisk for another 30 seconds to bloom the spices. Slowly pour in the chicken broth while whisking constantly to avoid lumps, then let the mixture simmer for 2-3 minutes until it thickens slightly. I find this gradual approach prevents lumps and creates a silky sauce base. Add the first 1/2 cup of monterey jack cheese and whisk until melted and smooth.
Working with one tortilla at a time, place it on a clean surface and spoon about 1/3 cup of the chicken filling from Step 1 down the center of each tortilla. Roll it tightly but gently, then place it seam-side down in your prepared baking dish, arranging the enchiladas snugly in a single layer. Continue until all 9 tortillas are filled and arranged—they should fit snugly, which helps them hold their shape during baking.
Remove the white sauce from Step 2 from heat and let it cool for about 1 minute—this prevents the sour cream from curdling. Whisk in the sour cream until smooth and fully incorporated, then gently fold in the green chiles. Pour this creamy sauce evenly over the rolled tortillas, making sure to coat them well. Sprinkle the remaining 3/4 cup of monterey jack cheese over the top for a golden, melty finish. I always save some cheese for the top rather than mixing it all into the sauce—it creates those delicious browned, crispy cheese edges.
Bake the enchiladas uncovered at 350°F for 22-25 minutes, until the sauce is bubbling around the edges and the filling is heated through. Turn the oven to broil and position the baking dish 4-6 inches from the broiler element. Broil for 2-3 minutes, watching closely, until the cheese on top is golden brown and slightly charred in spots—this adds flavor and creates an irresistible texture contrast. Remove from the oven and let rest for 2-3 minutes before serving.