Prepare the grill for indirect cooking over medium heat (350° to 450°F).
Wash the squashes under cold water. Using a heavy, sharp knife, cut the ends off of each squash and then cut each squash into four or six pieces. Using a tablespoon, scoop out and discard the seeds and pulp. Place the squash pieces on a sheet pan and brush the flesh with the oil. Season with salt and pepper.
Brush the cooking grates clean. Grill the squash pieces, skin side down, over indirect medium heat, with the lid closed, for about 30 minutes. Meanwhile make the glaze
In a small saucepan over medium heat, combine the glaze ingredients and cook until the butter is melted and the glaze is smooth, about 2 minutes, stirring often. Remove from the heat.
After the first 30 minutes of cooking, return the squash pieces to the sheet pan. Close the grill’s lid to maintain the heat inside. Brush the flesh with the glaze, return the squash to the grill, and continue to roast over indirect medium heat, with the lid closed as much as possible, until soft and tender, 30 to 40 minutes, glazing every 15 to 20 minutes. Season with more salt, if desired. Drizzle with the remaining glaze and serve warm.
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