1. Adjust oven rack to lower-middle position and heat oven to 450 degrees. Arrange short ribs bone-side down in single layer in large flameproof roasting pan; season with salt and pepper. Roast until meat begins to brown, about 45 minutes; drain off all liquid and fat with bulb baster. Return pan to oven and continue to cook until meat is well browned, 15 to 20 minutes longer. (For flanken-style short ribs, arrange ribs in single layer in large roasting pan; season with salt and pepper. Roast until meat begins to brown, about 45 minutes; drain off all liquid and fat with baster. Return pan to oven and continue to cook until browned, about 8 minutes; using tongs, flip each piece and cook until second side is browned, about 8 minutes longer). Transfer ribs to large plate; set aside. Drain off fat to small bowl and reserve. Reduce oven temperature to 300 degrees. Place roasting pan on two stovetop burners set at medium heat; add wine and bring to simmer, scraping up browned bits with wooden spoon. Set roasting pan with wine aside.

2. Heat 2 tablespoons reserved fat in large Dutch oven over medium-high heat; add onions, carrots, and celery. Sauté, stirring occasionally, until vegetables soften, about 12 minutes. Add garlic and cook until fragrant, about 30 seconds. Stir in flour until combined, about 45 seconds. Stir in wine from roasting pan, chicken stock, tomatoes, rosemary, thyme, bay leaves, tomato paste, and salt and pepper to taste. Bring to boil and add short ribs, completely submerging meat in liquid; return to boil, cover, place in oven, and simmer until ribs are tender, about 2 to 2 1/2 hours. Transfer pot to wire rack and cool, partially covered, until warm, about 2 hours.

3. Transfer ribs from pot to large plate, removing excess vegetables that may cling to meat; discard loose bones that have fallen away from meat. Strain braising liquid into medium bowl, pressing out liquid from solids; discard solids. Cover ribs and liquid separately with plastic wrap and refrigerate overnight. (Can be refrigerated up to 3 days.)

4. To prepare garnish and finish dish: In Dutch oven, cook pancetta or bacon over medium heat until just crisp, 8 to 10 minutes; remove with slotted spoon to plate lined with paper towel. Add to Dutch oven pearl onions, sugar, and salt; increase heat to high and sauté, stirring occasionally, until browned, about 5 minutes. Spoon off and discard solidified fat from reserved braising liquid. Add defatted liquid and bring to simmer, stirring occasionally; adjust seasoning with salt and pepper. Submerge ribs in liquid, return to simmer. Reduce heat to medium and cook, partially covered, until ribs are heated through and vegetables are tender, about 5 minutes longer; gently stir in Pancetta or bacon. Divide ribs and sauce among individual bowls, sprinkle each with 1 tablespoon parsley, and serve.