In a large skillet, heat oil over medium-high heat. Add onion, bell pepper, celery, and garlic; season with salt and pepper. Cook, stirring frequently, until vegetables are softened, 5 to 7 minutes.
Add ground beef to skillet. Cook, breaking up meat with a wooden spoon, until it is no longer pink, 6 to 8 minutes.
Stir tomato sauce, ketchup, and Worcestershire sauce into beef mixture in skillet. Simmer until thickened, stirring occasionally, 6 to 8 minutes.
Season the mixture with more salt and pepper, as desired. Spoon onto buns, and serve immediately.
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