Cut clean potatoes with skin on into ½" thick rounds.
In a large saucepan, bring potato slices to a boil in salted water and cook about 12 minutes until slices are tender crisp. Do not over cook. Drain potato slices and set aside. (Can be done in advance and refrigerated till ready to BBQ).
While potatoes slices boiling bring the rice vinegar to a boil in a microwaveable cup. Add mustard seeds and set aside to allow the mix to cool completely.
Prepare a double sheet of heavy foil large enough to hold the potatoes in a single layer and large enough to fold up a a ½" rim around the edge. Make sure the rim will hold all the melted butter so it doesn't drip through to the grill. Distribute butter in chunks evenly around the foil.
Preheat the grill and set to medium heat. Transfer the foil to the grill and allow butter to melt. Spread potato slices evenly in a single layer around the foil.
Allow potato slices to cook without disturbing them until the bottoms are evenly browned- about 19-12 minutes. Gently turn potatoes and allow the other side to brown slightly. (Depending on the level on heat on your BBQ - ensure at least one side is browned and crispy. If potatoes are getting too cooked forego browning the other side.)
Whisk the remaining vinaigrette ingredients into the mustard seed mix. Season to taste with salt and pepper.
Transfer the potatoes to a large bowl. Add the celery, green onions and fresh tarragon. Toss while warm with the vinaigrette. Season salad lightly with salt and pepper if desired. Serve immediately.
Leftovers can be refrigerated a day or two. Rewarm gently in microwave or oven before serving.