Bring a large pot of water to a boil, then season the water with salt and cook the penne al dente. Heads up: you will need to reserve a ladle or two of the starchy cooking water, 1/2 to 3/4 cup, before draining the pasta.

Place half of the peas in the bottom of a serving dish. Place the rest of the peas in a food processor with the pine nuts, basil, tarragon, garlic, lemon zest, cheese, and olive oil. Add a little salt and pepper, then process into a coarse paste. Adjust the seasonings.

Pour the reserved pasta water over the peas in the serving bowl, then add the pesto. Pour the hot, drained pasta over the peas and pesto and toss vigorously to coat and combine. Adjust the seasoning and serve, passing extra cheese at the table.