Preheat the oven to 350 degrees.
Wash the bell peppers and slice the tops off. Remove the stem and seeds from the inside.
In a small bowl, combine the ketchup, water, vinegar, brown sugar, Worcestershire sauce, mustard, garlic powder, and onion powder. Stir until smooth. Set aside.
Add the ground beef to a large skillet and brown over medium heat. Drain the fat and return to the skillet. Add the corned beef hash to the pan and cook until heated through.
Add the sloppy joe sauce to the pan with the beef and stir to coat.
Spoon the meat mixture into each of the 4 bell peppers and place in an 8x8 baking dish. Cover with foil and bake for 30 minutes.
Remove the foil and top each pepper with the cheese. Continue baking for another 10 minutes, uncovered, or until the peppers have softened to your liking.