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Warm a large Dutch oven or large stock pot over high heat for a minute or two. Season beef with a pinch of salt and pepper. Add the beef to the pot. Brown the beef on two sides in two batches, takes about fifteen minutes. Once the beef is browned add it to a plate and set off to the side.
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Reduce heat to medium. Sauté mushrooms for three minutes. Add in the carrot and celery, sauté another three minutes, stirring with a wooden spoon or rubber spatula. Add the onion, sauté an additional two minutes. Add garlic cook for a minute. Add the beef back to the pot.
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Add the butter and stir in until it melts. Add the flour, stir to combine. Cook flour and butter for a minute.
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Pour in the beef stock and tomatoes. Add the thyme and bay leaf. Stir to combine the flour butter mixture into the soup. Bring to a simmer.
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Add in the barley once the soup is simmering. Cover with lid and let the soup simmer over medium/low heat for 45 – 60 minutes, until barley is puffed and tender.
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Remove bay leaf and thyme stems. Stir in fresh parsley and remove from heat. Let the stew cool for five minutes before serving.
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Stew lasts 3 – 4 days in the refrigerator in an airtight container. Soup will last up to a month in an airtight container in the freezer.