Preheat the oven to 325°F and set a rack in the lower middle position.
Pat the beef dry and season with salt and pepper. In a large Dutch oven or heavy soup pot, heat 2 tablespoons of olive oil over medium-high heat until shimmering.
Add beef to the Dutch oven. Cook, turning occasionally, until meat is well browned on 2 sides, about 10 minutes. Transfer beef to a rimmed baking sheet or large plate and set aside. (To sear the meat properly, let the meat develop a nice brown crust before turning with tongs.) Transfer the beef to a large plate and set aside.
Add the onions, garlic, balsamic vinegar, soy sauce, and Worcester sauce; cook, stirring with a wooden spoon and scraping the brown bits from the bottom of the pan, for about 5 minutes. Add the tomato paste and cook for a minute more. Sprinkle with the flour. Stir until the flour is dissolved, 1 to 2 minutes.
Add the beef with its juices back to the pan. Add the chicken broth, water, bay leaf, thyme, and sugar. Stir with a wooden spoon to loosen any brown bits from the bottom of the pan, and bring to a boil. Cover the pot with a lid, transfer to the preheated oven, and braise for 2 hours 20 minutes.
Remove the pot from the oven and add the carrots, parsnips, and potatoes. Cover and place back in oven for about 40 minutes more, or until the vegetables are cooked, the broth is thickened, and the meat is tender.
Remove beef from the broth and place it on a cutting board. Use forks, shred beef, and remove any big chunks of fat. Add shredded beef back into broth
Fish out the bay leaf and discard, then taste and adjust seasoning, if necessary. Add the shredded beef back into the pot and carefully stir in with the broth and vegetables.
Serve the stew warm, or let it come to room temperature, and then store in the refrigerator overnight or until ready to serve. Reheat, cover, and cook over medium heat. Garnish your classic beef stew with fresh parsley, if desired.