1. Preheat grill to medium-high. Mash avocado with lime juice, salt and pepper. Stir in cilantro and adjust seasoning to taste. Cover and set aside.
2. Place beef patties on grill. Cook, turning as needed, for 12 to 15 minutes or until cooked through. Brush pineapple rings, on both sides, with BBQ sauce. Grill for 2 to 3 minutes per side or until well marked.
3. Meanwhile, fry eggs until sunny side up or to desired level of doneness. Season with salt and pepper.
4. Place lettuce on bottom half of each bun. Top with a grilled pineapple ring, a slice of ham, guacamole, a beef patty and a fried egg. Cap with top bun and serve immediately.
5. Serve with hot sauce for those who like it spicy.