Bring a large pot of salted water to a boil. Add the pasta and cook as the label directs, adding the peas during the last 4 minutes of cooking. Reserve 1 3/4 cups cooking water, then drain.
Heat the butter and olive oil in a large skillet over medium-high heat. Add 1 cup of the reserved cooking water and 2 teaspoons pepper. Increase the heat to high and boil until the liquid is reduced by half, about 3 minutes.
Add the pasta and peas to the skillet and simmer, tossing, until well coated. Remove from the heat and sprinkle with the parmesan, pecorino and parsley; toss until the cheese melts and the sauce is creamy, adding the remaining 3/4 cup cooking water as needed to loosen. Top each serving with more cheese.