Pat the stewing beef dry with paper towels and season with salt and black pepper.
Heat the olive oil in a large Dutch oven set over high heat. Add the beef to the pot in a single layer (you may need to cook your beef in two batches to prevent overcrowding) and cook just until the beef starts to brown on the outside - about 3-5 minutes.
Once all the beef has been browned, return all the beef to the pot, reduce heat to medium, and sprinkle with two tablespoons of all-purpose flour. Cook for about a minute, continuously mixing the beef to evenly distribute the flour. Remove the beef to a clean plate and set aside.
Heat an additional tablespoon of olive oil in the same pot or Dutch oven set over medium heat. Add the mirepoix (onions, carrots, celery) and cook for about 10 minutes. Scrape up any brown bit stuck to the bottom of the pot and cook with the vegetables (those brown bits are loaded with yummy flavor!)
After the vegetables have started to soften, add the cubed potatoes, fresh garlic, fresh oregano, tomato paste, and Worcestershire sauce. Gently mix to combine.
Return the seared beef back to the pot and add the beef broth, water, and barley. Mix well to combine and increase to high heat. Bring to a boil, then cover and reduce the heat to medium-low. Add bay leaves. Simmer for at least 1 hour, stirring occasionally.
Once the vegetables are soft, the barley is tender, and the beef melts in your mouth, remove from heat and season with additional salt, pepper, and fresh oregano, to taste. Enjoy!