Place the white and red potatoes into a large pot of boiling salted water and cook for 20 to 30 minutes, until they are just cooked through.  Just before draining, add green beans to the pot and let cook for about a minute.  Drain in a colander and place a towel over the potatoes to allow them to steam for 10 more minutes. As soon as you can handle them, cut in 1/2 (quarters if the potatoes are larger) and place in a medium bowl. Toss gently with the wine and chicken or vegetable stock (or water mixed with bouillon). Allow the liquids to soak into the warm potatoes before proceeding.

Mix the vinegar, mustard, 1/2 teaspoon salt, and 1/4 teaspoon pepper together and slowly whisk in the olive oil. Add the vinaigrette to the potatoes. Add the scallions, parsley, basil, 1 1/2 teaspoons salt, and 1/2 teaspoon pepper and toss. Serve warm or at room temperature.