Prepare barbecue grill and preheat for direct, medium-high heat (the charcoal or gas flame is directly under the cooking area, and you can hold your hand just above grill level only 3 to 4 seconds).
For charcoal grill: Before you put the grill over the hot coals, brush it with a light coat of oil.
For gas grill: When hot, brush grill with a light coat of oil.
While grill heats, cut pineapple crosswise into 1/2-inch-thick slices; cut out the core from each slice and discard.
In a small bowl, mix brown sugar and lime juice; brush onto both sides of pineapple slices with a pastry brush.
Lay pineapple slices on lightly oiled grill (close lid on gas grill) and cook, turning once with a wide spatula, until pineapple is hot and tinged with brown on both sides, about 8 minutes total.
With spatula, transfer 1 or 2 pineapple slices to dessert bowls; top with a scoop of ice cream and sprinkle equally with coconut and peanuts, if desired.