Make a quick mayonnaise. Pulse the egg yolk, dijon mustard, and lemon juice in a blender with a few quick pulses. Turn the blender on and drizzle in the oil in a thin, steady stream. Continue to blend until the mixture is light in color and thick.
Blend the herbs and garlic. Stop the blender and scrape down the sides. Add the parsley, chives, tarragon, anchovy paste, and garlic. Blend until smooth and vibrant green.
Place the greek yogurt or sour cream in a medium bowl. Add the herb mayonnaise and stir to combine.
Taste the dressing for seasoning. The anchovy paste is usually salty enough, but add additional salt if desired.