Bring a large pot of water up to a boil then season water with salt and cook penne to al dente. Heads up: you will need to reserve 1 or 2 ladles of starchy cooking water, 1/2 to 3/4 cup, before draining the pasta.
Place 1/2 of the peas in the bottom of a large serving dish. Place the rest of the peas in a food processor with the pine nuts, basil, tarragon leaves, lemon zest, cheese and olive oil. Add a little salt and pepper then process the pesto into rough paste, adjust seasonings.
Pour starchy water over peas in bowl then add pesto. Pour hot, drained pasta over the pesto and toss vigorously to coat and combine. Adjust seasoning and serve, passing extra cheese at the table.