Cook pasta according to package directions until al dente. Reserve ½ cup pasta water before draining.
While pasta cooks, add garlic, avocados, basil, parsley, heavy cream, olive oil, lemon juice, salt, and 2 tablespoons Parmesan to a food processor or blender.
Blend until completely smooth and creamy.
Drain pasta without rinsing and immediately toss with avocado sauce.
Add reserved pasta water gradually until desired consistency is reached.
Garnish with remaining Parmesan cheese and additional fresh herbs.