In a large skillet, cook chorizo , onions and garlic until meat is browned. Stir in black beans, tomatoes, spinach . Simmer until almost all the liquid is gone, stirring occasionally.
Place peppers in a high sided baking dish and fill with chorizo mixture. Cover dish with foil and baked until peppers are fork tender, approximately 45 minutes ( I started checking at 30 minutes). Remove pan from oven and turn on broiler. Put a slice of fresh mozzarella or the shredded cheese on each pepper and return to broiler. Cook long enough to melt cheese to your satisfaction. That can be as little as 3 minutes for shreds or as long as 10 minutes for the fresh mozzarella depending on your oven and how far away the pan is from the broiler element.
Once cheese is to your satisfaction remove and let sit for 5 minutes to let the temperature stabilize. Sometimes if you eat food straight from under the broiler you can singe your mouth.