Heat canola oil in a large skillet over medium-low heat. Add chopped onions and green peppers and sauté for about 5 minutes until they begin to soften.
Push the vegetables to the outer edge of the pan and increase heat to medium-high. Add ground beef to the center of the pan, spreading it in an even layer. Let it cook undisturbed for 5 minutes until it begins to brown on the bottom.
Season the beef with salt and pepper, then flip it over. Continue cooking, breaking the meat into small pieces with a wooden spoon or spatula, until no longer pink and fully cooked, about 2-3 minutes more.
Reduce heat to medium-low and add ketchup, yellow mustard, Worcestershire sauce, and sugar. Stir to combine all ingredients thoroughly.
Simmer for 2-3 minutes until flavors meld and sauce reaches desired consistency.
Serve hot on hamburger buns, brioche buns, or potato rolls.