Put the broccoli, garlic, walnuts and cheese in a food processor, and pulse to a thick, green rubble.
Add the olive oil, lemon juice and sea salt, blitz briefly to make a thick sauce, then set aside.
Reserve a mugful of pasta water, then return the pici to the pan and gently stir in the broccoli pesto, adding the pasta water a tablespoon at a time to loosen the sauce as needed.