Step 1: In a large skillet over medium-high heat, warm the olive oil. Add the chopped onion and bell pepper, stirring occasionally until they soften and achieve a slight golden hue, approximately 10 to 15 minutes.
Step 2: Incorporate the ketchup, cooking and stirring occasionally until the mixture darkens and the ketchup reduces to a thick paste, about 7 to 10 minutes.
Step 3: Introduce the minced garlic and chili powder, cooking and stirring until fragrant, roughly 1 minute. Then, add the apple cider vinegar, yellow mustard, brown sugar, and Worcestershire sauce. Season with salt and black pepper, continuing to cook while stirring frequently until well combined, about 1 additional minute.
Step 4: Raise the heat to high and add the ground beef. Using a fork, break apart the beef until it is fully crumbled and free of large lumps. Cook, stirring frequently, until browned, approximately 5 minutes.
Step 5: Pour in the canned tomato sauce and bring the mixture to a boil, stirring to ensure everything is thoroughly combined. Allow it to cool slightly and adjust seasoning with salt if necessary.
Step 6: Serve the beef mixture generously on toasted hamburger buns, dividing it evenly among them. Enjoy your Sloppy Joes!