Peel the sweet potatoes and cut them lengthwise into ¾-inch-thick slices. Bring 3 quarts of water to a boil and add the sweet potato slices. Simmer until they are just starting to soften, about 12 minutes. Drain and let cool in a single layer on a large platter.
Combine the butter, honey, cinnamon, and nutmeg in a small saucepan and place over low heat, stirring to combine. Brush the potato slices on both sides with the butter mixture and season to taste with salt and pepper.
Prepare enough coals for a medium-hot charcoal fire, or preheat your gas grill on medium-high for 10 minutes with the lid closed.
When the coals are ready or the gas grill is hot, grill the sweet potato slices for about 6 minutes, turning once, until they are soft through the middle and nicely browned.