Bring a large pot of salted water to a boil. Add the pasta and cook as the label directs. Reserve 1 1/2 cups cooking water, then drain.
Heat the olive oil, 2 tablespoons butter, 1/2 cup of the reserved cooking water, 1 teaspoon pepper and the peas in the same pot over medium-high heat. Cook, shaking the pot occasionally, until the peas are tender and the butter melts, 2 to 4 minutes.
Return the pasta to the pot along with the remaining 2 tablespoons butter, the parmesan and 3/4 cup cooking water. Stir until creamy, adding the remaining cooking water as needed to loosen. Stir in the arugula, basil and mint. Divide among bowls.
Mix the ricotta and lemon zest in a small bowl; season with salt and pepper. Dollop on each serving of pasta. Drizzle with olive oil and season with more pepper.