In a food processor, combine the garlic, anchovy, lemon juice, and salt. Slowly add in olive oil a few drops at a time to emulsify. You are essentially making a type of aioli (mayonnaise without raw egg).
Add yogurt, and chopped herbs and process until smooth. Taste for seasoning, and adjust salt, pepper and lemon juice as needed. Cover and chill in refrigerator while you prep the remaining ingredients for the Platter. You can keep prepared Green Goddess Dip in a tightly sealed container in the refrigerator for three days.
Assemble the Board:
Place small bowls with dips on the platter or board near the edges or corners.
Arrange lettuce wedges, endive leaves, cucumbers, radish, avocados, sugar snap peas, fennel, olives, cornichons, tortilla chips, asparagus spears, broccoli, green beans on a large cutting board, cheeseboard, tray, or platter.
Garnish with oregano, fresh basil, and chopped fresh parsley if using.