For the balsamic reduction: Combine the balsamic vinegar and sugar in a medium saucepan. Bring to a boil, reduce the heat and simmer until reduced by three-quarters of its original volume. Set aside to cool.
For the parsnip puree: place the parsnips in a heavy-bottomed saucepan, add enough heavy cream to cover and bring to a slow boil. Reduce the heat and simmer until the parsnips are cooked. Place in a blender and process until smooth. Season to taste with salt and pepper.
Next, carefully remove the connective tissue found on the side of each scallop, if applicable. Pat dry with a paper towel and season both sides with salt and pepper. In a small saute pan, heat 2 tablespoons of the olive oil over high heat to smoke point, then place half of the dry, seasoned scallops in the pan, being careful to not splash the oil. When the scallops are golden brown and have released from the pan, turn over and sear on the opposite side. Add half of the carrots, half of the butter and half of the thyme to the pan. When the butter begins to foam, lower the heat and carefully angle the pan so the butter is to one side, and baste the scallops while they finish cooking. Repeat the process with the rest of the scallops in a new pan or quickly rinse the previous pan.
In a bowl, mix the arugula with a touch of lemon juice, truffle oil and salt.
Serve the scallops on a warm plate over the parsnip puree. Garnish the plate with baby carrots, truffled arugula and the balsamic reduction.
When blending hot liquid, first let it cool for five minutes or so, then transfer it to a blender, filling only halfway. Put the lid on, leaving one corner open. Cover the lid with a kitchen towel to catch splatters, and pulse until smooth.