Heat the vegetable oil in a large skillet over medium heat. Add the yellow onion and green bell pepper and cook, stirring, until softened, 4–5 minutes; add the garlic and cook until fragrant, 30 seconds.
Add the ground beef, kosher salt, and black pepper. Cook, breaking the meat into small crumbles, until browned with no pink remaining, 5–7 minutes; drain excess fat if needed.
Stir in the canned tomato sauce, ketchup, tomato paste, Worcestershire sauce, brown sugar, yellow mustard, apple cider vinegar, chili powder, and red pepper flakes. Simmer over medium-low, stirring occasionally, until thick, glossy, and spoonable but not runny, 10–15 minutes.
Spread the cut sides of the hamburger buns with the unsalted butter and toast in a skillet over medium heat until golden at the edges, 2–4 minutes. Spoon the beef mixture onto the toasted buns and serve with pickle chips, if using.