Bring large pot of water to a boil over medium heat.
Preheat the oven to warm, about 200 degrees F. Put a large serving bowl or a platter, for the pasta, into the oven to warm.
In a small pot over low heat, add the saffron threads and the stock. Let steep until ready to use.
When the water boils, season with salt, add the pasta and cook to al dente. Just before draining, add a ladle of the starchy pasta water to the pot with the saffron stock. Drain the pasta.
Remove the bowl or platter from the oven and scatter with the butter pats. Add the pasta and pour in the saffron liquid. Sprinkle with half of the cheese and toss for 1 minute. Add more cheese and continue to toss for another 1 to 2 minutes. Keep tossing until the pasta is evenly coated and cheese has melted into the saffron broth forming a creamy, lightly golden sauce. Serve immediately.