Pat the roast dry with paper towels. Remove all visible fat and any silver skin. Cut into 1-inch pieces and season with salt and pepper.
Add 1 tablespoon vegetable oil to a large Dutch oven or heavy bottom soup pot. Warm over medium-high heat until shimmering. Add half the beef and cook until browned on one side. Stir and continue cooking until the beef is well seared and brown on all sides, about 10 minutes.
Transfer browned beef to a bowl using a slotted spoon; cover to keep warm. Repeat with the remaining beef and transfer to the bowl, keep warm. (For the best flavor, sear the beef over high heat so it browns and forms crusty bits on the bottom of the pot.)
Add the remaining tablespoon of oil to the now empty Dutch oven. Add the onions and carrots and cook, stirring frequently, until vegetables are softened and the onion starts to brown and caramelize, about 8 minutes. Add the garlic, thyme leaves, paprika, red pepper flakes and tomato paste to the vegetables. Sauté for 1 minute or until the garlic is fragrant. Add one cup of broth to deglaze the bottom of the pot scraping up any browned bits.
Add all browned beef, remaining broth, tomatoes and barley to the pot. Bring to a boil. Cover and reduce the heat to medium/medium-low. Simmer, stirring occasionally, until the beef and vegetables are tender, about 1 hour.
Add the soy sauce and cook for 5 minutes. Remove from the heat. Allow the soup to rest for a few minutes. Using a large spoon or ladle, skim off any fat pooled on top, if desired. This may not be necessary if your roast was well trimmed and not overly fatty. Stir in the parsley, check seasoning and add salt and pepper to taste. Serve with crusty bread for sopping up the broth.