Melt the unsalted butter in a medium (10-inch) saute pan or Dutch oven over medium-low heat. Add the leeks and saute for 8 to 10 minutes, stirring occasionally, until tender but not browned. Add the potatoes, celery root, heavy cream, 2 teaspoons salt, and 1 teaspoon pepper and bring to a boil. Lower the heat to very low, cover the pan, and simmer gently for 25 to 30 minutes, stirring occasionally, until the vegetables are tender. Be careful?don't let the vegetables scorch on the bottom of the pan!
In two batches, pour the leek and potato mixture into the bowl of a food processor fitted with the steel blade and pulse until coarsely pureed. Return the puree to the saute pan, stir in the truffle butter, taste for seasonings, and keep warm over very low heat. If the puree gets too thick, add a little more heavy cream.
If it hasn't already been removed, peel off the tough strip of muscle on the side of each scallop. Pat the scallops dry with paper towels and season them generously on both sides with salt and pepper. Heat a large (12-inch) saute pan over medium-high heat. Add the grapeseed oil and, when the oil is almost smoking hot, add the scallops in a single layer. Cook undisturbed for about 3 minutes, until golden brown on the bottoms. Don't crowd the scallops or they'll steam rather than sear. Using a small metal spatula, turn the scallops and cook for 2 to 3 minutes more, until just cooked through.
Spoon the warm puree onto 3 dinner plates. Place the scallops on the puree, drizzle with the basil oil, and sprinkle with the chives. Serve warm.