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Boil potatoes in salted water until fork-tender, about 15–20 minutes. Drain, then mash with butter, milk, and salt. Cover and keep warm.
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While potatoes cook, brown ground beef and chopped onion in a skillet over medium heat until fully cooked. Drain excess grease if needed.
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Sprinkle flour over beef mixture and cook 1–2 minutes, stirring.
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Gradually stir in beef broth. Bring to a simmer and cook until thickened, about 5 minutes.
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Stir in garlic powder, onion powder, salt, pepper, heavy cream, and Worcestershire sauce. Taste and adjust seasoning.
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Heat green beans with sliced red onion until warmed through.
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Spoon hamburger gravy over mashed potatoes and serve with green beans on the side.