Combine half of the caraway, the garlic, salt and pepper in a bowl. Place pork in a glass baking dish. Rib pork with spice mixture. Cover and chill up to 24 hours.
Preheat oven to 350 degrees F. In a large skillet, heat 1 tablespoon of the olive oil over medium high heat. Add onion, carrots, bay leaves, and half of the remaining caraway; saute until soft (8 minutes). Transfer to a roasting pan. in the same skillet, heat 1/2 tablespoon olive oil over high heat. Add half of the cabbage and half of the remaining caraway. Saute until the cabbage wilts. Add to onion mixture. Repeat with remaining cabbage. Season entire cabbage onion mixture with salt and pepper.
In the same skillet, heat 1 tablespoon olive oil over high heat. Add pork; brown on all sides (10 minutes). Set atop the vegetables in pan. Add beer and molasses to skillet; bring to a boil, scraping browned bits. Pour over vegetables. Add broth.
Roast pork and vegetables for 45 minutes. Turn pork over and roast until thermometer inserted into thick part registers 150 degrees F (45 more minutes). Place pork on cutting board. Discard bay leaves. Using slotted spoon, place vegetables on platter. Slice pork; place atop vegetables. Transfer cooking juices to a small saucepan. Boil 5 minutes. Spoon over pork.