Chop fingerling potatoes in halves or thirds.
In a pot, pour cold water and salt and add chopped fingerling potatoes and bring to boil then simmer and cook until fork tender but still firm. Drain water from potatoes using a strainer and run cold water to cool instantly. Shake off excess water, place in a bowl and set aside.
To make dressing, in a medium sized bowl, add mayonnaise, white wine vinegar, pesto, capers, Dijon mustard, lemon juice, lemon zest and black pepper and whisk together until fully combined.
Chiffonade basil into thin strips.
To assemble, in the bowl of cooled cooked potatoes, add in pesto dressing and gently toss together. Sprinkle grated parmesan cheese and basil on top. Serve family style.