Heat your oven to its lowest setting, then place a large pasta platter or bowl inside to warm. Bring a large pot of water to a boil, salt it, add the pasta and cook until al dente. Drain, reserving a ladleful of the pasta cooking water.
While the pasta is working, in a medium saucepan, bring the chicken stock and saffron to a boil and cook until reduced to about 1 cup, about 10 minutes.
In a medium skillet, heat the EVOO, 1 turn of the pan, over medium-high heat. Add the zucchini and cook until crisp-tender, about 5 minutes.
Remove the platter from the oven and scatter the butter on it. Add the pasta, zucchini and saffron-infused stock, then add the cheese and toss vigorously for 1 minute to form a yellow, glossy sauce. Add the reserved pasta cooking water as desired if the sauce is too thick.