1To make the butter; combine the butter, pecans, maple syrup, cinnamon, salt, ginger, and pepper in a small bowl. Mix well with a fork.
2With a large, heavy knife, cut the squash in half lengthwise. Remove the seeds with a spoon. Lightly brush the exposed flesh with the olive oil. Season with salt and pepper to taste.
3Put the squash halves, cut side down, on the cooking grate and grill indirectly over high heat until grill marks are clearly visible, about 30 minutes. Turn the squash halves cut side up. Spread the exposed flesh with the pecan butter. Continue grilling indirectly over high heat until the flesh is tender, 20 to 30 minutes. Serve warm.