In a large skillet, heat the oil over medium heat. Add the onions and bell peppers and cook, stirring occasionally, until soft, about 6 to 8 minutes.
Add the beef and break up with a wooden spoon. Cook until no longer pink, about 10 to 12 minutes. If desired, remove the excess grease by tilting the skillet to one side, and remove the grease with a large spoon into a small bowl. Leave about 1 to 2 tbsp in the skillet.
Add the beef stock, tomato sauce, chili sauce, Worcestershire sauce, mustard, vinegar, brown sugar, salt, and pepper and bring to a simmer, stirring to fully incorporate.
Reduce the heat to medium and simmer for 20 minutes until most of the liquid has reduced down, stirring occasionally.
Toast the buttered buns (a couple minutes under the broiler...but keep an eye on them!)
On a baking sheet, add a mound of meat mixture for each sandwich you are preparing. Place a handful of cheese on top of each mound of meat. Place under the broiler until cheese has melted. Keep an eye on them, don't let them burn!
Use a spatula to transfer the sloppy joe mounds topped with melted cheese onto the bun bottoms. Add the top bun and serve at once!