Prepare beef roast. Pull roast apart at its major seam (delineated by lines of fat) into two halves. Use knife as necessary. With knife, remove large knobs of fat from each piece, leaving thin layer of fat on meat. Tie three pieces of kitchen twine around each piece of meat to keep it from falling apart.
Adjust oven rack to middle position; heat oven to 300 degrees. Thoroughly pat beef dry with paper towels; sprinkle generously with salt and pepper. Place pancetta in 8-quart heavy-bottomed Dutch oven; cook over medium heat, stirring occasionally, until browned and crisp, about 8 minutes. Using slotted spoon, transfer pancetta to paper towel-lined plate and reserve. Pour off all but 2 tablespoons fat; set Dutch oven over medium-high heat and heat fat until beginning to smoke. Add beef to pot and cook until well browned on all sides, about 8 minutes total. Transfer beef to large plate; set aside.
Reduce heat to medium; add onions, carrots, celery, and tomato paste to pot and cook, stirring occasionally, until vegetables begin to soften and brown, about 6 minutes. Add garlic, sugar, flour, and reserved pancetta; cook, stirring constantly, until combined and fragrant, about 30 seconds. Add wine and tomatoes, scraping bottom of pan with wooden spoon to loosen browned bits; add thyme sprig, rosemary, and parsley. Return roast and any accumulated juices to pot; increase heat to high and bring liquid to boil, then place large sheet of foil over pot and cover tightly with lid. Set pot in oven and cook, using tongs to turn beef every 45 minutes, until dinner fork easily slips in and out of meat, about 3 hours.
Transfer beef to cutting board; tent with foil to keep warm. Allow braising liquid to settle about 5 minutes, then, using wide shallow spoon, skim fat off surface. Add minced thyme, bring liquid to boil over high heat, and cook, whisking vigorously to help vegetables break down, until mixture is thickened and reduced to about 3 1/2 cups, about 18 minutes. Strain liquid through large fine-mesh strainer, pressing on solids with spatula to extract as much liquid as possible; you should have 1 1/2 cups strained sauce (if necessary, return strained sauce to Dutch oven and reduce to 1 1/2 cups). Discard solids in strainer. Season sauce to taste with salt and pepper.
Remove kitchen twine from meat and discard. Using chef's or carving knife, cut meat against grain into 1/2-inch-thick slices. Divide meat between warmed bowls or plates; pour about 1/4 cup sauce over and serve immediately.