1. Combine avocado, lemon juice, parsley, basil, scallions, garlic and anchovies, if desired, in a food processor. Process, stopping and scraping down sides of bowl as needed, until smooth, with some green flecks remaining. Add mayonnaise and sour cream. Pulse to blend. Season with salt and pepper.
2. Transfer dip to a bowl, cover and chill for at least 2 hours. Taste and season with salt and pepper. Serve with assorted crudités for dipping.