Heat a large skillet over medium heat. Add the ground beef and cook until some of the fat starts to render, which should take about 3 to 4 minutes. Incorporate the chopped onion and green bell pepper, continuing to cook until the vegetables are tender and the beef is fully browned, approximately another 3 to 5 minutes.
Mix in the ketchup, brown sugar, mustard, and garlic powder, then season with salt and pepper to your preference. Reduce the heat to low and let the mixture simmer gently for 20 to 30 minutes, allowing the flavors to meld together.
Spoon the meat mixture evenly onto the split hamburger buns, and serve immediately.
Notes
If you're using ground beef with a higher fat content than lean, make sure to drain off any excess fat before beginning Step 2.