Preparation:
Preheat oven to 350ºF. Spread walnuts on rimmed baking sheet; toast until slightly brown, about 7 minutes; set aside.
Meanwhile, cook pasta according to package directions; drain, reserving 1/4 cup pasta cooking water.
To prepare pesto: In bowl of food processor, combine avocado, parsley, lemon zest and juice, garlic, salt and reserved walnuts; pulse until coarsely chopped. Add olive oil; pulse to desired consistency.
In large serving bowl, toss pasta with Pesto and cheese; add 2 tablespoons or more of pasta cooking water if needed.