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.
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.
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 4 to 5 hours).
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.
Cook's Country Notes: TWO ROASTS ARE BETTER THAN ONE.
Use two smaller roasts for this recipe, because the meat cooks more quickly and the small roasts are easier to manage in the slow cooker—and to find in the supermarket. Most boneless pork shoulder roasts come bound in string netting, which is difficult to remove after cooking. We prefer to cut the netting off before cooking, trim the roasts and then tie each one with cooking twine. If you cannot find 2 1/2- to 3-pound pork shoulder roasts, you can substitute one 6-pound pork shoulder roast.
Remove the netting from the pork roasts. Open each roast and trim any excess fat.
Tie the roasts separately. To ensure even cooking, fold the smaller lobes under, then tie each roast with kitchen twine every 1 1/2 inches around the circumference and once around the length.