Make the dip: Combine the parsley, sour cream, chives, tarragon, anchovies, lemon juice, garlic, shallot, 1/2 teaspoon salt and a few grinds of pepper in a blender and puree until smooth. Scrape into a bowl and gently stir in the mayonnaise. Cover and refrigerate at least 2 hours or overnight.
Arrange red and green veggies on a platter. Serve with the dip.