Preheat oven to 325 degrees and start a large pot of water to boil.
In a large skillet, saute onion and garlic for 3-5 minutes.
Add rice, meat, salt, and pepper. Stir to mix well. Remove from heat.
Take the cabbage and pound the core end against the countertop to loosen. Remove core and discard.
Place the whole head of cabbage into the boiling water. Cover and cook for 3 minutes.
Remove softened outer leaves and discard. Separate the large leaves from one another and trim out the thick center stem from each one.
One at a time, put 1 rounded tablespoonful of the meat & rice mixture into the center of a leaf. Roll up leaf and place seam side down into a large greased baking pan. (Do not make more than 2 layers).
Combine the beef broth and mushroom soup and pour over cabbage rolls.