Place the cabbage in a pot of boiling water on the stovetop, turning it often with tongs, or a knife stuck into the core.
Remove the outer leaves as they become tender little by little, and set aside.
Heat the olive oil in a skillet over medium heat and cook the onions until they begin to become tender.
Add the ground beef, cooked rice, onions, eggs, garlic powder and salt and pepper to taste to a mixing bowl, and use your hands to combine it well.
Place ⅓ of a cup of the meat mixture into each cabbage leaf, fold the edges into the middle and fold the ends in to form a packet around the meat mixture.
Put the filled cabbage leaves open side down into a 9×13 baking dish.
Preheat the oven to 325 degrees.
Mix together the tomato soup, diced tomatoes, broth and salt and pepper to taste in a bowl.
Pour the tomato mixture over the cabbage rolls in the casserole dish.
Cover the casserole dish with aluminum foil and bake for 2 hours.
