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Grate onion over breadcrumbs in a large bowl. Let sit 5 minutes to absorb moisture.
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Add remaining patty ingredients except olive oil to the bowl. Mix gently with your hands until just combined. Don’t overmix.
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Shape mixture into 6 oval patties, about 1-inch thick. Press a slight dimple in center of each.
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Heat olive oil in a large skillet over medium-high heat. Sear patties 3-4 minutes per side until nicely browned. Remove to a plate.
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In same skillet, melt butter. Add diced onion and cook until softened, about 3 minutes.
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Add mushrooms and garlic. Cook until mushrooms release their moisture and start to brown, 5-7 minutes.
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Sprinkle flour over vegetables, stir and cook 1 minute.
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Gradually whisk in beef broth, Worcestershire sauce, and Dijon. Bring to simmer.
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Return patties to skillet, including any juices from plate. Cover and cook 10-12 minutes until patties are cooked through and gravy thickens.
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Season gravy with salt and pepper to taste. Garnish with parsley if desired.
