Make ¼ inch-deep slashes between ribs on both sides of spareribs slab.
In a food processor or blender, combine onion, garlic, jalapeno peppers, allspice, ginger, oil, nutmeg and salt.
Whirl until pureed.
Rub spice purée over surface and into slashes on both sides of spareribs slab.
Cover and let stand for 1 to 2 hours (or refrigerate until next day).
Barbecue ribs by indirect heat.
Distribute bay leaves over meaty sides of ribs; then place ribs, meat side up, on grill directly above drip pan.
Cover barbecue and adjust dampers as necessary to maintain an even heat.
Cook until ribs are well browned on outside and meat near bone is no longer pink; cut to test (1 to 1¼ hours).
Near end of cooking time, prepare Lime-Dressed Avocado; also cut papaya into wedges.
To serve, cut spareribs into 2 to 3-rib portions.
Arrange on a large platter with avocados and papayas.