Heat oven to 425F.
Split squash lengthwise and place cut-side down on a baking sheet. Roast 45 minutes-1 hour, until the squash flesh is very tender.
Meanwhile, heat stock or water in a small pot with the saffron threads to bloom the saffron and infuse the liquid with flavor.
While squash roasts, heat EVOO, a couple of turns of the pan, in a pan over medium heat. Add onions, carrot, garlic and chili pepper, and season with salt and pepper. Cook 8-10 minutes then add saffron stock and tomatoes to the pan. Crush tomatoes with a potato masher or spoon. Add oregano, parsley and basil, and simmer to thicken, 20-30 minutes over medium-low heat.
When the squash is done, melt butter in small pot. Flip squash over and shred the squash into spaghetti-like strands with a fork, leaving the flesh in the squash shells. Dress evenly with melted butter, cheese, salt and pepper.
Top each half-squash with sauce and more cheese, and serve.