1) Boil the potatoes whole until tender, about 10 minutes. Drain and cool to room temperature. Peel and cut the potatoes into bite-size pieces, discarding the potato skins.
2) Put the hot dogs into a hot griddle pan and cook until golden brown, about 10 minutes. Cool the hot dogs to room temperature, then cut them crosswise into bite-sized pieces.
3) Toss the potatoes, parsley, basil and olive oil in a large bowl. Season the potato salad with salt and pepper, to taste. Add the hot dogs to the salad and toss. Season to taste, adding additional olive oil if the salad seems too dry.