Combine the avocado, Greek yogurt, mayonnaise, parsley, chives, tarragon, lemon juice, rice vinegar, garlic, anchovies, salt, and pepper in the bowl of a food processor or high-speed blender.

Pulse the mixture 5 to 10 times to break down the larger herb leaves and avocado chunks.

Process on high speed for 30 to 45 seconds until the emulsion is completely smooth and vibrant green.

Scrape down the sides of the bowl and pulse again to ensure all herbs are fully incorporated.

Check the consistency; if too thick, add water or olive oil one teaspoon at a time until the desired pouring consistency is achieved.

Taste and adjust seasoning with additional salt or lemon juice if necessary.

Transfer to an airtight container and chill for at least 30 minutes to allow flavors to meld before serving.