Heat a large non-stick frying pan over medium-high heat. Add ground beef, onion, 3/4 tsp of salt and 1/4 tsp of pepper, and cook, stirring occasionally, for 5 minutes, or until cooked through.
Put shredded cabbage, eggs, 3/4 tsp of salt and 1/4 tsp of pepper in a large bowl and mix until combined.
Spray a non-stick 9x13 inch baking dish with cooking spray.
Put half of the cabbage mixture in a baking dish and spread in a layer. Add the beef mixture on top of the cabbage mixture and spread in a layer. Add the remaining cabbage mixture and spread in a layer. Sprinkle the casserole with shredded cheese.
Put the beef and cabbage casserole in the oven and bake for 45 minutes.