Bring a large pot of water to a boil for the pasta. Place stock in small pot with saffron over low heat to warm.
Heat EVOO, 2 turns of pan, in large skillet over medium heat with butter. When butter foams, add shallots and season with salt and pepper. Stir 2-3 minutes; add lemon zest, garlic and poppy seeds, and stir 1-2 minutes. Deglaze with wine and reduce until almost evaporated. Add warm saffron stock and cream, let reduce while pasta cooks.
Cook pasta in salted boiling water to al dente. Reserve half a cup of starchy water and drain pasta. Toss with sauce, using reserved water as needed to incorporate the cheese and sauce into a thick coating on pasta. Add lemon juice and parsley; adjust salt and pepper. Serve.