Preheat oven to 375°F and spray a 9x13-inch baking dish with cooking spray.
In a large skillet, cook ground beef and diced onion over medium-high heat until beef is browned and onion is tender, about 8 minutes. Drain fat.
Stir in black beans, green chiles, cumin, chili powder, and garlic powder. Cook for 2 minutes more.
Spread 1/2 cup enchilada sauce on the bottom of the prepared baking dish.
Layer one-third of the tortilla quarters over the sauce, followed by one-third of the beef mixture, one-third of the remaining enchilada sauce, and one-third of the cheese.
Repeat layers two more times, ending with cheese on top.
Cover with foil and bake for 25 minutes.
Remove foil and bake for an additional 10 minutes until cheese is golden and bubbly. Let stand 10 minutes before serving with sour cream and green onions.