Put the potatoes in a large pot and cover with salted water. Bring to a boil, reduce the heat to a simmer, cover and cook until fork-tender, about 30 minutes. Drain and let cool completely. Slice the potatoes about 1/4-inch (6mm) thick.
In a large bowl, combine the mayonnaise, scallions, mustard, tarragon, parsley, lemon juice, 1 teaspoon salt and the pepper. Add the potatoes and toss gently to combine.