1. Allow frozen peas to thaw in a colander for 1-2 hours.
  2. Cook pasta al dente in plenty of boiling water with salt in 10-12 minutes.
  3. Meanwhile, mash half the peas, basil and cheese with whipped cream into a fine sauce in a food processor. Dilute the sauce with a dash of the cooking water. Add salt and freshly ground pepper to taste.
  4. Pick the leaves of the twigs from the remaining basil.
  5. Drain pasta, collect cooking water. Stir the pea sauce and the remaining peas into the pasta and heat the pasta until the dish is warm. Add some cooking water if necessary.
  6. Serve pasta with sauce in warm, deep plates and sprinkle basil leaves on top. Add the rest of the Parmesan cheese.