Heat a large skillet over medium-high heat. Cook and stir ground beef, onion, and garlic in the hot skillet until beef is browned and crumbly, 5 to 7 minutes. Drain and discard grease. Add 4 cups water and beef base; stir to combine. Add tomato sauce, Worcestershire sauce, pepper, celery salt, and marjoram; bring to a simmer.
Add carrots and simmer for 35 minutes. Add potatoes and green beans; cook until tender, about 15 minutes.
Meanwhile, mix flour and 2 tablespoons water together in a small bowl until no longer lumpy, adding more water if necessary. Stir into stew and simmer until thickened, 5 to 10 minutes.
You can use fresh or frozen green beans.
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