1. Pat roasts dry with paper towels and season with salt and pepper. Heat 2 teaspoons oil in large skillet over medium-high heat until just smoking. Brown roasts all over, about 10 minutes. Transfer to slow cooker.
2. Add onions and additional 2 teaspoons oil to empty skillet and cook until browned, about 5 minutes. Add garlic and tomato paste and cook until fragrant, about 1 minute. Stir in wine and simmer, scraping up any browned bits with wooden spoon, until thickened, about 2 minutes. Stir in tapioca, tomatoes and thyme; transfer to slow cooker.
3. Toss carrots, parsnips, 1/4 teaspoon salt, 1/4 teaspoon pepper, and remaining oil in bowl until vegetables are well coated. Scatter vegetable mixture over pork. Cover and cook on low until meat is tender, 9 to 10 hours (or cook on high for 4 to 5 hours).
4. Transfer roasts to cutting board, tent with foil, and let rest 10 minutes. Remove twine from roasts and cut meat into 1/2-inch thick slices; transfer to serving platter. Using slotted spoon, transfer carrots and parsnips to platter with pork. Stir vinegar into sauce and season with salt and pepper. Serve, passing sauce at table.