Bring a large pot of water to a boil, salt it, add the pasta and cook until al dente. Drain, reserving 1/2 cup of the pasta cooking water.
While the pasta is working, in a small saucepan, bring the chicken stock and saffron to a boil. Lower the heat to a low simmer to keep warm.
In a deep skillet with a tight-fitting lid,heat the EVOO, 4 turns of the pan, over medium heat. Stir in the chiles and garlic for 3 to 4 minutes. Add the tomatoes and saffron stock, cover and cook over medium-high heat, shaking the pan occasionally, until the tomatoes burst, about 10 minutes. Remove the lid and mash the tomatoes a bit with a potato masher. Stir in the parsley.
Toss the pasta with the sauce and a handful of cheese. Add a splash of the reserved pasta cooking water to combine. Serve the pasta in shallow bowls; top with more cheese, if desired.