In a large skillet over medium heat, heat oil. Once hot, add bell pepper and onion and cook until soft, about 5 minutes. Stir in garlic and tomato paste and cook until fragrant, about 1 minute.
Add ground beef and cook until no longer pink, breaking up with a wooden spoon into crumbles, for about 6 minutes. Add the Worcestershire sauce, tomato sauce, ketchup, brown sugar, and apple cider vinegar. Stir well and bring to a simmer. Cook for 15-20 minutes or until thickened to desired consistency.
Serve on hamburger buns with onions and pickle chips.