Soak the threads of saffron in 1 tablespoon of hot water for 8 to 10 minutes. Meanwhile, bring a large pot of salted water to a boil.
Melt the butter in a large skillet over medium heat.
Add the garlic and cook, stirring occasionally, for about 2 minutes.
Add the cream, mix in the saffron mixture, and increase the heat to medium-high.
Simmer until slightly thickened, about 2 to 3 minutes. Stir in the lemon zest.
Add the pasta to the boiling water and cook until just undercooked.
Remove ½ cup cooking water, then drain the pasta and transfer to the skillet with the sauce and finish cooking the pasta in the sauce adding reserved pasta water as needed to loosen.
Remove from the heat and stir in the Parmesan cheese and lemon juice. Add a splash of pasta water to thin the sauce as needed.
Taste for seasoning and add salt & pepper to taste.