Put the potatoes in a medium saucepan, cover with cold water, add a sprinkle of salt, and bring other a boil over medium-high heat. Cook for about 15 to 20 minutes, or until they are just tender and easily pierced with a small sharp knife. Drain and set aside until they are cool enough to handle.
In the meantime, add two tablespoons of the olive oil to a small skillet over medium heat. When the oil is hot, add the chopped shallot and cook for about a minute or two. Then add the minced garlic and cook for a few moments more. Remove the pan from heat.
In a small bowl, whisk together the remainder of the olive oil, white wine, dijon mustard, salt, and pepper.
When the cooked potatoes are cool enough to handle, but still warm, slice them about ¼ inch thick. Then transfer to a bowl.
Pour the dressing over the warm sliced potatoes. Add the shallot and garlic mixture as well. Then toss gently to coat.
Allow the potatoes to sit for about 15 to 20 minutes in order to soak up the dressing, tossing occasionally.
Transfer the potato salad to a serving bowl. Scatter the chopped parsley and chives over the top and serve warm or room temperature.