Heat olive oil in a large, high-sided pan or skillet over medium heat. Add the onion, minced garlic, and green pepper to the pan and season with salt and black pepper to taste. Stir to combine and sauté for 4-5 minutes, or until the vegetables soften and start to develop some color.
Add the ground beef to the pan and break it into small pieces with a spatula. Cook for 5-6 minutes until the meat is thoroughly browned. Remove from the heat and carefully drain any excess fat from the skillet.
Return the pan to the heat and add the tomato sauce, tomato paste, Worcestershire sauce, brown sugar, mustard, and chili-garlic sauce. Season with additional salt and pepper if desired. Stir thoroughly to combine, simmer, uncovered for 5-10 minutes until heated through.
Preheat the broiler/grill while the meat simmers. Arrange the hamburger buns on a large, rimmed baking sheet. Brush each one with melted butter and place under the broiler for a few minutes until the buns are golden brown.
Remove buns from the broiler and arrange them on plates. Spoon the warm meat sauce onto the bottom half of each bun. Cover and serve immediately with your choice of sides. Enjoy!