Bring a large saucepan of water to a boil over high. Carefully add eggs with a slotted spoon. Cook exactly 9 minutes, and, using slotted spoon, remove eggs, and immediately plunge into a bowl of ice water. Let stand 15 minutes. Peel eggs, and halve lengthwise. Separate yolks from whites, reserving both.
Process yolks, avocado, tarragon, parsley, vinegar, mayonnaise, salt, pepper, and anchovies in a food processor until smooth, about 1 minute. Spoon or pipe filling into egg white halves. Garnish with tarragon and parsley.
