Dry the beef with paper towels, then season with salt and pepper. Heat 2 teaspoons of the oil in a 12-inch skillet over medium-high heat until just smoking. Brown half of the beef, about 10 minutes, then add to the slow cooker. Return the skillet to medium-high heat and repeat with 2 more teaspoons oil and the remaining beef.
Add the remaining 2 teaspoons oil to the empty skillet and heat over medium heat until shimmering. Add the onions, carrots, and 1/4 teaspoons salt. Cook until the vegetables are softened, about 5 minutes. Stir in the wine, scraping up any browned bits. Simmer until the wine has reduced by half, about 1 minute, then pour into the slow cooker.
Add the tomatoes with their juice, the broths, thyme and barley to the slow cooker. Cover and cook, on either low or high, until the beef is tender, 6-7 hours on low or 4-5 hours on high. Before serving, stir in parsley and season with salt and pepper to taste.
TO MAKE AHEAD: The night before (or a day in advance) prepare the recipe through step 2. Instead of adding the ingredients to the slow cooker, refrigerate them, but be sure to store the browned meat in one container and the vegetables and wine in another container. In the morning, add the chilled ingredients to the slow cooker, then add the tomatoes with their juice, the broths, thyme and barley to the slow cooker. Proced with step 3. The cooking time will run to the high end of the range given in the recipe.