Wash and dry potatoes, then peel and cut them into small, evenly-sized pieces. Place into a large pot of cold, salted water and bring to a boil. Reduce heat and cook potatoes until fork tender, about 15 minutes. Remove from heat, drain and transfer to a medium bowl. Set aside.
To make avocado dressing: Add all ingredients to a food processor and pulse until well incorporated.
Add dressing to the bowl of potatoes and lightly smash. Garnish with avocado pieces and cilantro.