Method:
Heat olive oil in skillet. When hot, add onions and peppers and cook until tender. In another bowl, combine beef, eggs, Worcestershire, salt and pepper. Mix lightly and shape into 12 thin patties. Spoon onion and pepper mixture onto centers of 6 patties and top each with 2 tablespoons ketchup or chili sauce and a bit of oregano. Cover with remaining patties and pinch the sides securely closed; place in refrigerator until ready to cook.
When you're ready and the grill is hot, grill burgers about 3 inches from the coals for about 5 to 8 minutes on each side. Top with a slice of cheese when you're just about done; cover the grill to melt the cheese. Serve burger on bun with tomatoes, lettuce and the condiments of your choice.