Finely chop basil, walnuts, and garlic in food processor. Gradually add olive oil while machine is running and process until smooth. Mix in 1/4 cup Parmesan cheese.
Transfer the pesto to a small jar. (Pesto can be prepared 3 days in advance. Pour enough olive oil over sauce to cover. Cover and refrigerate).
Bring cream to slight boil in medium saucepan. Be careful not to burn the cream. Once cream begins to boil, whisk in pesto. Season sauce with remaining 1/4 cup Parmesan in large bowl.
Toss to coat pasta evenly and serve.