Add the pasta to a pan of boiling water. Bring back to the boil and simmer fast for 9 minutes, stirring now and then. Add the petit pois for the last 5 minutes. Drain and reserve 4tbsp cooking water. Return to the pan.
While the pasta is cooking, heat the oil and cook the mushrooms, stirring often.
Add the chives, ham, creme fraiche and mustard to the mushrooms and heat until simmering.
Season with pepper and simmer for 1 minute. Add to the pasta with the reserved cooking water and toss together. Serve immediately with grated Parmesan and ground black pepper.