Wash and halve or quarter the small red potatoes. Place them in a large pot, cover with water, and bring to a boil. Cook for 15-20 minutes until tender, then drain and cool.

In the final minutes of cooking the potatoes, add trimmed snap peas to the pot for a quick blanch for 2-3 minutes. Transfer to ice water, drain, and set aside.

In a blender, combine avocado, mayonnaise, parsley, buttermilk, chives, lemon juice, tarragon, anchovies, and shallots. Blend until smooth, adjusting consistency with more buttermilk as needed.

In a mixing bowl, combine cooled potatoes, blanched snap peas, chopped celery, and celery leaves. Pour dressing over and toss gently to coat.

Cover with plastic wrap and refrigerate for at least 30 minutes before serving.