Named for their resemblance to the nut of an oak tree, acorn squash have a tough, inedible skin and dense, fibrous flesh with a distinct, slightly-sweet flavor. A member of the family of winter squashes that includes butternut, pumpkin and spaghetti squash, the vegetable is frequently halved, stuffed with a savory dressing and baked. The vegetable's character stands up well to both sweet and savory seasonings, and grilling them adds a layer of roasted flavor.
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Prepare the grill for indirect heat cooking. If you’re using a charcoal grill, light the briquettes and, when they’re covered with ash, move them to one side. For a gas grill, light one side of the grill until it reaches high heat -- around 500 degrees Fahrenheit.
Cut the squash in half from stem end to blossom end, and use a spoon to scrape out the seeds and fibers in the center. Discard the seeds and fibers. Cut the halves of the squash into slices about two inches thick. Brush the squash slices with olive oil and sprinkle them with salt and pepper.
Place the slices on the grill over the hot coals, or the hot side of a gas grill, and cook them, turning with tongs every few minutes, until they’re deep brown, or just beginning to char. Move the slices to the cool side of the grill, cover and let them cook until they’re tender. Depending on the size of the slices, this should take between 10 and 20 minutes. Remove and serve.