Place a large stock pot or cast iron soup pot on the cooktop and add the olive oil.
Using a large mixing bowl or gallon-size Ziploc bag, add stew meat and season well with salt and pepper.
Sprinkle flour over stew meat and coat well.
Returning to your pot, turn the heat to medium-low and add the stew meat in batches, adding more oil as necessary and being careful not to overcrowd. Cook until the meat starts to brown on either side, about 1 minute. Place each finished batch on a plate and set aside.
Add more olive oil if necessary, and add your carrots, celery, and onion. Scrape the bottom of the pot to remove the brown bits.
Cook on medium-low until vegetables have softened, stirring occasionally, about 7-10 minutes.
Mix in your Italian seasoning, garlic, and tomato paste. Stirring frequently, cook on low until garlic is aromatic, 2-3 minutes.
Return the beef to the pot.
Carefully pour in the beef broth and water, scraping up all the bits on the bottom of the pot.
Add your bay leaf, pour in your barley, and combine.
Bring the heat to medium-high and boil for 2-3 minutes. Turn the heat down to medium or medium-low, with the lid cracked, and cook at a simmer for 45 minutes to 1 hour or until barley and beef are cooked. Stir occasionally.
Once the barley and beef are cooked, remove bay leaf, ladle into bowls, add chopped parsley, optional, and serve hot with crusty bread.