Place a large pot of water on stove to boil for the pasta.
In a 2-3 quart pot, combine the EVOO, butter, stock and garlic, and bring to a boil. Once the liquids come to a boil, add peas and simmer about 3 minutes. Transfer half the peas to a food processor and pulse into a thick puree. Add herbs, lemon juice and cheese, and pulse again 6-8 beats, to combine.
Salt boiling water and cook pasta to 1 minute less than al dente, and reserve about ¾ cup starchy water before draining. Drain pasta and add back to hot pot with sauce, reserved peas and hot cooking water. Toss to combine, and add more cheese and adjust seasonings as necessary. Transfer to a large bowl and top pasta with cress.