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Heat the grill to high.
Brush the pineapple on both sides with the oil and place on the grill. Grill until golden brown and caramelized on both sides, about 6 minutes. Remove from the grill, stack the slices and cut into chunks. While the pineapple is grilling, place the pound cake on the grill until lightly golden brown on both sides, about 20 seconds on each side. Remove the pineapple from the grill and, when cool enough to handle, either slice or cut into chunks.