Preheat oven to 350°F (175°C) and lightly grease a 9x13 inch baking dish.
In a large skillet over medium-high heat, cook ground beef and onion until beef is thoroughly browned and onions are translucent.
Add garlic, cumin, chili powder, salt, and pepper; cook for 1 minute then remove from heat and set aside.
In a medium saucepan, melt butter over medium heat; whisk in flour and cook for 2 minutes to form a blonde roux.
Gradually whisk in chicken broth, stirring constantly to prevent lumps, and simmer until the sauce has thickened.
Remove the saucepan from heat and whisk in the sour cream and diced green chiles until the sauce is uniform.
Lay a tortilla flat and place 3 tablespoons of the beef mixture and 2 tablespoons of shredded cheese in the center.
Roll the tortilla tightly and place it seam-side down in the prepared baking dish. Repeat for all tortillas.
Pour the creamy white sauce evenly over the top of the rolled enchiladas.
Sprinkle the remaining shredded cheese over the sauce.
Bake for 20 to 25 minutes until the sauce is bubbling and the cheese is melted and lightly golden.