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Let a large skillet get heated over medium heat; add in the oil; then add in the onion, carrot, celery, and garlic; stir/saute 5-7 minutes or until softened.
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Stir in the tomato paste, tomato puree, vinegar, molasses, and Worcestershire sauce; bring to a simmer.
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Lower heat to low and let simmer gently for 45-60 minutes or until thickened and the flavors have melded.
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Add in a little water if the sauce gets too thick or dry.
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In another large skillet over med-high heat, brown the ground beef, breaking the meat apart into small pieces; cook until the meat is no longer pink; drain.
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Add the sauce to the meat and simmer over med-low for at least 10 minutes or until the flavors blend.
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Serve by spooning ½ cup of the filling over half a toasted hamburger bun and topping with the other half.