MICROWAVE BONES: Cut meat from bones and set aside. Arrange bones in 13- by 9-inch baking dish and microwave until well browned, 10 to 15 minutes. Transfer to slow cooker.
BROWN MEAT: Pat meat dry with paper towels and season with salt and pepper. Heat oil in large skillet over medium-high heat until just smoking. Cook meat until well browned, about 5 minutes per side. Transfer to slow cooker.
COOK AROMATICS: Cook onions, carrot, and celery in now-empty skillet over medium heat until browned, about 8 minutes. Stir in tomato paste and thyme and cook until beginning to brown, about 1 minute. Stir in wine and vinegar and simmer, scraping up any browned bits, until reduced to 1 cup, about 5 minutes. Stir in broth, tapioca, and bay leaves and return to boil. Transfer to slow cooker.
BRAISE AND FINISH: Cover slow cooker and cook on low until meat is fork-tender, about 8 hours (or cook on high for 4 to 5 hours). Transfer meat to serving platter. Strain and defat cooking liquid and discard solids. Stir parsley into sauce and season with salt and pepper. Pour 1 cup sauce over meat. Serve, passing remaining sauce at table.