In a large bowl, combine beef, allspice, chili powder, cinnamon, cloves, ginger, pepper, salt, and sugar. Form meat into 8 patties.
Grill hamburgers over medium-high heat until hamburgers reach medium-well temperature, about 8-10 minutes. Keep burgers warm.
Grill pineapple rings over medium-high heat, turning once until pineapple has grill marks, about 5 minutes.
In a medium bowl, mash avocado with garlic, lime juice, and salt and pepper to taste.
Assemble the burgers: Place a lettuce leave on a hamburger bun and top with smashed avocado, warm burger, and grilled pineapple ring. Place bun top on top. Repeat with remaining burger ingredients. Enjoy burgers immediately!