In a small saucepan, place the potatoes and cover with water. Set over high heat and bring to a boil, reducing to a low boil until tender, about 7 to 8 minutes. Remove from the heat and cool under cold running water. Once cool enough to handle, slice the potatoes into 1/4-inch rounds and place in a medium bowl. Set an 8-inch saute pan over medium heat and add the olive oil. When the oil is hot, add the shallots and garlic and saute until fragrant, about 1 minute. Add the sliced potatoes to the pan, and saute for 2 to 3 minutes. Add the balsamic vinegar to the pan and cook until reduced by about half, about 2 minutes. Season the potatoes with the salt and pepper and garnish with the chives and tarragon. Set aside while you prepare the scallops.
Potato Truffle Sauce and Scallops:
In an 8-inch saute pan set over medium heat, add 1 tablespoon of the butter. Once melted, add the shallots and garlic and saute until fragrant, about 1 minute. Add the potatoes and stock to the pan and bring to a boil, reduce to a simmer and cook until the potatoes are tender and the stock has reduced by about half, about 15 minutes. Season the potatoes with 1/2 teaspoon of salt and 1/4 teaspoon of the pepper. Place in a food processor with the heavy cream and pulse until well blended and smooth. Remove to a heat-proof glass or stainless steel bowl and fold in the truffle oil. Wrap with plastic wrap and set aside to keep warm while you prepare the scallops.
Set a 10-inch saute pan over high heat. Add the olive oil. While the oil is getting hot, Season the scallops with the remaining teaspoon of salt and 1/2 teaspoon of pepper. Dredge the scallops in the flour and shake to remove any excess flour. Place the scallops in the saute pan and sear for 2 minutes on the first side. Add the remaining 2 tablespoons of butter to the pan and swirl to evenly distribute. Turn the scallops and continue to cook for 1 1/2 to 2 minutes on the second side, or until golden brown and just cooked through. To serve, divide the potato sauce among the centers of 4 shallow bowls or plates. Place 3 scallops on top of the potato sauce, and garnish with the warm potato relish and chopped chives. Serve immediately.