1. In large bowl, combine meat, onion, 1 cup tomato sauce, thyme, salt and pepper. Mix well.
2. Pour 1/4 cup tomato sauce into bottom of 5-quart slow cooker.
3. Cut out core from cabbage and carefully remove leaves. Place a golf ball-sized mound of meat mixture into center of large cabbage leaf, edges curling upward. Starting with the thickest side, fold leaf over meat mixture, burrito-style. Place fold side down into slow cooker. Repeat with remaining meat and cabbage leaves, stacking as necessary.
4. Pour beer over cabbage rolls. Pour remaining tomato sauce on top of rolls.
5. Cook on LOW 5 hours. Halfway through cooking time, push cabbage rolls under broth to submerge them. Season to taste with salt and pepper before serving. Sprinkle with chopped parsley, if desired.
Tip
For a thicker sauce, remove cabbage rolls and add 2 tablespoons cornstarch to remaining liquid. Bring to a boil. Cook until desired thickness.
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