In a large pot of boiling salted water, cook pasta until al dente, about 12 minutes. Drain thoroughly and return to pot. Toss pasta with oil to prevent sticking.
While pasta is cooking, heat 1 Tbsp. butter in a large nonstick skillet over medium heat. Add onion and cook, stirring, until it's translucent, 5 minutes. Add prosciutto and cook for 2 minutes. Add peas and cook for 3 minutes.
Toss mixture with pasta in pot, along with remaining 5 Tbsp. butter, Parmesan, salt, pepper and lemon peel. Heat through.
Serve pasta with more cheese if desired.