Step 1: Heat a large skillet or Dutch oven over medium-high heat. Add olive oil. Once shimmering, add ground beef. Break it up with a spoon and cook until no pink remains, about 5-7 minutes. If using higher fat beef, drain any excess grease.
Step 2: Reduce the heat to medium. Add diced yellow onion and green bell pepper to the skillet with the cooked beef. Cook, stirring occasionally, until the vegetables soften, about 5-7 minutes.
Step 3: Stir in minced garlic and tomato paste. Cook for 1 minute, stirring constantly, allowing the tomato paste to caramelize slightly.
Step 4: Pour in ketchup, water, Worcestershire sauce, apple cider vinegar, light brown sugar, and yellow mustard. Stir everything together until well combined. Add salt and black pepper, or to taste.
Step 5: Bring the mixture to a gentle simmer. Reduce the heat to low, cover the skillet, and let it simmer for at least 10-15 minutes, allowing the flavors to meld and deepen. Stir occasionally to prevent sticking. If the sauce becomes too thick, add a splash more water.
Step 6: While the sloppy joe mixture simmers, lightly toast the hamburger buns. You can do this in a dry skillet, under the broiler, or in a toaster oven for a minute or two until golden.
Step 7: Spoon a generous amount of the warm sloppy joe mixture onto the toasted bottom half of each bun. Top with the other half of the bun and serve immediately.