Cook the tagliatelle in a large saucepan of salted, boiling water until al dente; usually 8-10 minutes.
Meanwhile, bring another saucepan of salted water to the boil and blanche the carrots and the courgettes for 1 minute. Drain and leave to cool to one side. Drain the tagliatelle when ready and transfer back to the saucepan.
Add the mangetout, carrots, courgette, parsley and olive oil and toss well. Season to taste then spoon into serving bowls. Garnish with the shave Parmesan before serving.