Heat oil in a large skillet or Dutch oven over medium-high. Sprinkle beef with pepper and 1 tablespoon salt. Add beef to skillet; cook, turning occasionally, until browned on all sides, about 12 minutes.
Transfer beef to a 6-quart slow cooker. Add sliced onions and garlic to skillet; cook, stirring occasionally, until onions are just softened, about 4 minutes. Stir in tomato paste; cook 1 minute. Stir in ½ cup water, scraping up browned bits from bottom of skillet. Pour onion mixture into slow cooker. Add carrots, beer, onion soup mix, thyme, and brown sugar.
Cover and cook until roast is fork-tender, 4 to 6 hours on HIGH or 8 to 10 hours on LOW. Stir in vinegar and the remaining 2 teaspoons salt. Transfer roast to a platter; shred into large chunks. Discard any large pieces of fat. Spoon vegetables onto platter around roast. Serve with mashed potatoes.
