Prepare the grill for direct and indirect cooking over medium heat (350° to 450°F).
Brush the cooking grates clean. Grill the sweet potatoes over indirect medium heat, with the lid closed, until tender when pierced with a fork, about 1 hour, turning three or four times. Remove from the grill and, when cool enough to handle, cut the potatoes in half lengthwise. Remove and discard the skins. Place the potatoes in a medium bowl and cover with foil.
Brush the onion slices with oil and season evenly with salt and pepper. Grill over direct medium heat, with the lid closed as much as possible, until tender, 10 to 12 minutes, turning once or twice. Remove from the grill and allow to cool. Cut into ¼-inch dice.
Using a mixer or potato masher, mash the potatoes with the butter until smooth. Add the diced onions and mix well. Season with more salt and pepper, if desired. Serve warm.
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