Pour water in baking dish and place halved squash cut-sides down in the dish.
Bake squash in preheated oven until a fork pierces the skin very easily, about 45 minutes. Let squash cook while preparing remainder of recipe.
Melt butter with olive oil in a large skillet over medium-high heat. Saute onion in hot butter until softened, about 5 minutes. Add garlic and continue to saute until fragrant, about 1 minute more. Pour diced tomatoes over the onion mixture; season with basil. Place a cover on the skillet, reduce heat to medium-low, and cook at a simmer until the tomatoes are soft, about 30 minutes; season with salt and pepper.
Once squash is cool enough to handle, use a fork to strip flesh from the skin in strands. Stir squash and Parmesan cheese into tomato mixture. Replace cover on skillet and cook until squash is heated through, 5 to 10 minutes more. Sprinkle additional Parmesan cheese over the dish to serve.