Bring a large pot of water to a boil, salt it, add the pasta and cook until al dente. Drain, reserving a couple of ladlefuls of the pasta cooking water.
In a food processor, puree half the peas with the basil, cheese, olive oil, pine nuts, tarragon and lemon peel until coarsely chopped. Season the pesto with salt and pepper.
In a large serving dish, pour 2/3 cup reserved pasta cooking water over the remaining peas, then stir in the pea pesto. Add the pasta and toss to combine. Serve in bowls and pass extra cheese around the table.