Add the watercress, basil, parsley, chives, tarragon, and garlic to the bowl of a food processor and pulse eight to 10 times to mix and chop. Scrape down the sides of the bowl and add in the lemon zest, lemon juice, goat cheese, mayonnaise, sour cream, Dijon, and anchovy paste and blend until everything is finely chopped and well combined.
Scrape down the sides of the bowl, give the dip another blend, and season with salt and pepper to taste.
Serve immediately with veggies, chips, and pita bread for dipping or cover and refrigerate until ready to serve. If you do refrigerate the dip, it will thicken up a little.