A dry, well-aged goat or sheep’s milk cheese may be substituted for the Parmesan cheese in this sauce. Don’t worry if this sauce separates; that’s part of its rustic charm.
Chop the walnuts in a food processor; use the pulse mechanism to avoid turning the walnuts into a purée. The pieces should be about the size of peppercorns.
Gently heat the chopped walnuts in the olive oil and cream. Do not let the sauce boil.
Stir in the grated cheese and the parsley. Simmer for 1 minute. Season with salt and pepper.