Brown beef: Get out a large pot (at least 6 quarts) and place the tablespoon of oil in it. Place the pot over medium-high heat and brown the beef in it. And by brown, I want to reiterate that it needs to actually get some of that brown seared look, not grey.
Add the onion, garlic, and herbs: Once the beef has been browned toss in the onions and let them cook until they become translucent. Then add in the minced garlic and herbs. Stir them in and let them cook for another minute.
Add in the tomato paste and flour, stir until they coat everything, and let them cook for another minute or two.
Deglaze the pot with the wine.
Add the stock, carrots, celery, tomato and bay leaf: Begin by pouring in the beef stock. Add just a cup of it at a time, and stir it so that the flour and tomato paste incorporates into the stock. After all of the stock has been added toss in the carrots, celery (including the heart), can of tomatoes, the bay leaf, and one cup of water. Stir this all up and let it come to a simmer
Cover the pot and let everything simmer for one to two hours.
Add in the green beans, potatoes, and barley. Cover the pot and continue to let everything simmer until the potatoes are tender. It should be about an hour.
Serve the beef and barley vegetable stew in a big bowl and enjoy.