1. Adjust oven rack to middle position and heat oven to 300 degrees. Thoroughly pat roast dry with paper towels; sprinkle generously with salt & pepper.
2. Heat oil in large heavy bottomed Dutch oven over medium-high heat until shimmering but not smoking. Brown roast thoroughly on all sides, reducing heat if fat begins to smoke, 8-10 minutes. Transfer roast to a large plate; sest aside. Reduce heat to medium; add the chopped onion, carrot & celery to pot and cook, stirring occastionally, until beginning to brown, 6-8 minutes. Add garlic and sugar; cook until fragrant, about 30 seconds. Add the chicken and beef broths and thyme, scraping bottom of pan with wooden spoon to loosen browned bits. Return roast and any accumulated juices to pot; add enough water to come halfway up the sides of the roast. Bring liquid to simmer over medium heat, then place large piece of foil over pot and cover tightly with lid; transfer pot to oven. Cook, turning roast every 30 minutes, until almost tender (about 3-3 1/2 hours), sharp knife should meet little resistence, add red potatoes, carrot chunks & parsnips (if using), to Dutch oven, submerging them in liquid. Continue to cook until vegetables are almost tender, 20-30 minutes.
3. Transfer roast to carving board; tent with foil to keep warm. Allow liquid in pot to settle, about 5 minutes, then use wide spoon to skim fat off surface, discard thyme sprig. Add wine, salt & pepper to taste; boil over high heat until vegetables are fully tender, 5-10 minutes. Using a slotted spoon, transfer to warmed serving bowl or platter. Using chef's or carving knife, cut meat into 1/2" thick slices or pull apart into large pieces; transfer to bowl or platter with vegetables, pour about 1/2 cup sauce over meat and vegetables. Serve, passing remaining sauce separately.