Season the ground beef with salt, black pepper, garlic salt, and dry mustard.
Heat a large skillet over medium-high heat. Add the seasoned beef and cook for 6 to 8 minutes, breaking it apart, until browned. Drain excess grease if needed.
Add the onion and red and green bell peppers. Cook for about 2 minutes, until the vegetables begin to soften.
Whisk the ketchup, Worcestershire sauce, brown sugar, salt, pepper, onion powder, and garlic salt in a bowl. Pour over the beef and simmer for 2 to 3 minutes.
Place a portion of the Sloppy Joe mixture in the center of each tortilla. Top with cheese sauce and shredded cheddar, then fold in the sides and roll tightly into a burrito.
Heat the vegetable oil in a clean skillet over medium heat. Grill the burritos seam-side down for about 1 minute per side, until golden and crisp. Serve hot.