Peel the sunchokes, slice them and place them in water immediately to keep them from oxidizing.
Melt the butter in a large pot over medium heat until it begins to foam. Reduce the heat to low, drain the sunchokes, and add them to the pot. Sweat for 5 minutes without browning. Add the stock, heavy cream, and thyme and simmer until the sunchokes are tender, about 30 minutes.
Remove and discard the thyme. Puree the sunchokes with their cooking liquid in a blender until smooth. Strain through a fine-mesh strainer and season with the salt, pepper, and smoked paprika.
Roast the hazelnuts in a small nonstick pan.
Remove the skins and then roughly chop them. Divide the sunchoke velouté between 2 bowls. Place the truffle slices in equal amounts over the soup. Sprinkle over the chopped hazelnuts and drizzle with the oil. Serve.
