Heat the sugar in a small saucepan with 2 teaspoons of water and the lemon peel until it melts. Simmer a little so that the water evaporates and the sugar becomes a little thick.
Peel and roughly chop the Jerusalem artichoke tubers. Place in an ovenproof dish so that they do not lie on top of each other. Drizzle with the olive oil, season with salt and pepper. Pour the lemon caramel and thyme leaves on top.
Simmer in the hot oven for about 30 minutes until the vegetables are nice and soft and browned in places.