Preheat your oven to 230C/450F.Gas 8. In a bowl mix together your creme fraiche, lemon juice, garlic, half the thyme and most of the Parmesan, and season well to taste. Thin out with around 6 to 8 tablespoons of water and throw in the sliced Jerusalem artichokes. Mix well and place everything in an ovenproof baking dish. Cover with tin foil and bake for 35 minutes.
Mix the bread crumbs, the remaining thyme and some salt and pepper with a touch of olive oil. Remove the artichokes from the oven, discard the foil and sprinkle the remaining Parmesan over the top. Then sprinkle the flavored bread crumbs over the Parmesan. Use up all the bread crumbs. Bake in the oven for about15 minutes until the bread crumbs are golden. If you're in a pokey pokey kind of mood you can poke the artichokes about a bit so some of the bread crumbs fall underneath them. This makes it look more rustic instead of like a crumble.