Cook the new potatoes in a saucepan of boiling water for about 10 minutes or until they are just tender. Drain and return them to the pan. Set over a low heat and shake them around for a few minutes to evaporate any moisture. Transfer the potatoes to a mixing bowl and leave to cool for about 5 minutes.
Sprinkle the vermouth or wine and wine vinegar over the potatoes. Season with pepper. Turn the potatoes to mix, then leave to cool completely.
Meanwhile, mix together the garlic, mayonnaise and yogurt in a small bowl until smooth.
When the potatoes are cool, add the cucumber, green onions, dill and tarragon. Spoon on the mayonnaise and yogurt mixture, and stir gently to mix everything together. Serve the new potato salad at room temperature or chilled, garnished with dill and tarragon leaves.