In a food processor (or blender), combine the scallions and chives. Season with salt and pepper. Add water and blend. Pour 5 tablespoons of the olive oil through the top of the food processor in a slow, steady stream. Taste for seasoning.
Bring the potatoes to a boil in a pot of water and reduce to a simmer. Season the water with a pinch of salt and add bay leaves. Simmer the potatoes until they are tender when pierced with the tip of a knife, about 20 minutes.
In a bowl large enough to hold the potatoes, whisk together the red wine vinegar, shallots, mustard, capers and tarragon. Whisk in the remaining olive oil. Taste for seasoning. Drain the potatoes of their cooking liquid and discard the bay leaves.
Place the potatoes in the bowl with the dressing and lightly crush them with the tines of a fork. Season lightly with salt and pepper and toss them in the dressing. Finish by adding the scallion and olive oil mixture. Stir to blend. Keep warm at room temperature until serving.