Heat oven to 400F.
Arrange tomatoes on a rimmed baking sheet and the squash on another. Dress tomatoes with 2 tablespoons EVOO, toss squash with 2 tablespoons EVOO. Season tomatoes with thyme, salt and pepper, squash with salt, pepper and a little nutmeg. Drizzle garlic with EVOO, season with salt and pepper, and wrap in a foil pouch. Roast garlic to soft and golden, 40 minutes; tomatoes until charred at edges and burst, 30 to 35 minutes (or longer depending on size); squash to golden and tender, 25-30 minutes.
Meanwhile, melt butter in a small pot over medium-low heat; add saffron and swirl. Add stock and keep at a low simmer.
Bring a pot of water to a boil. Salt water and cook pasta to al dente.
Squish garlic cloves into a large bowl. Mash in buttery stock; add tomatoes and mash with basil to create a sauce. Add pasta and squash, toss to combine; Add cheese, toss and serve.