Bring a large pot of heavily salted water to a boil and cook the pasta according to the package directions. In a small saucepan, boil the potatoes until very tender. When the pasta is cooked, drain and rinse under cold water. Drain the potatoes.
Make the dressing by placing the cooked and drained potatoes in a blender along with 3 tablespoons of pistachios, the garlic, olive oil, lemon juice and water. Blend until smooth and creamy.
Put the cooked pasta into a large mixing bowl; add the dressing, olives, sun-dried tomatoes, artichoke hearts, green onions, red pepper, celery and basil and toss to combine. Roughly chop the remaining pistachios and stir into the salad. Refrigerate until serving time. Can be made several hours ahead of time. Let come to room temperature before serving for best flavor.