Bring a large pot of water to a boil, salt it, add the pasta and cook until al dente. Drain, reserving 1 cup of the pasta cooking water.
While the pasta is working, in a large skillet, heat the EVOO, 5 to 6 turns of the pan, over medium heat. Add the anchovies and cook, stirring, until melted into the oil. Add the chile and garlic and cook, stirring, for about 3 minutes. Stir in the olives and lemon zest; season with pepper. Pour in the white wine (or vermouth) and stir to deglaze the pan, scraping up the browned bits.
Stir the reserved pasta cooking water, the lemon juice and parsley (or parsley and celery leaves) into the sauce in the skillet. Add the pasta and toss. Top with the cheese.