2 tablespoons good-quality olive oil, plus more for brushing the squash
Salt and pepper
2 tablespoons chopped garlic
2pounds fresh tomatoes, chopped
1/4cup chopped fresh basil
Freshly grated Parmesan for serving (optional)
Instructions
Start the coals or heat a gas grill for medium direct cooking. Make sure the grates are clean.
Cut the squash in half through the equator (not end to end). Remove the seeds with a spoon. Brush the cut sides and interior with oil and sprinkle with salt and pepper.
Put the squash on the grill directly over the fire, skin side down. Close the lid and cook, turning the squash every 10 minutes or so for even cooking, until the flesh is fork-tender, 40 to 50 minutes total; start checking it for doneness at 30 minutes. Turn the halves cut side down until browned, 5 to 10 minutes. Transfer to a plate. (The squash will stay hot in the skin for about 15 minutes.)
While the squash is on the grill, make the tomato sauce. Put the 2 tablespoons oil and the garlic in a large skillet over medium heat and cook until the garlic is fragrant and gently sizzling. Add the tomatoes, sprinkle with salt and pepper, and adjust the heat to a gentle bubble. Cook, stirring occasionally, until they cook down into a thickened sauce, 25 to 35 minutes; increase the heat to medium-high if your tomatoes throw off a lot of liquid. Taste and adjust the seasoning and keep warm. (Or you can make the tomato sauce up to a day or two ahead and gently reheat it when the squash goes on the grill.)
Stir the basil into the tomato sauce. Scrape a fork over the interior of the squash from bottom to top to remove the flesh from the skin and tease it apart into long strands. Put in a large serving bowl and toss with the tomato sauce to evenly coat the strands. Taste and adjust the seasoning. Serve hot, with Parmesan for sprinkling if you like.