In pot of salted boiling water, cook pasta until al dente. In large skillet, cook anchovies, garlic, and crushed red pepper in oil over medium, stirring often, until anchovies break down, about 6 minutes. Stir in pickled zucchini. Reserve 1 cup of pasta cooking water; drain pasta. Toss pasta and 1/2 cup cooking water with zucchini and anchovies in skillet; add more water if pasta is dry. Garnish with parsley and cheese.