Peel parsnips and potatoes, cut into pieces and cook in salted boiling water for 25 minutes.
In the meantime, butter out a gratin dish. Drain and puree the parsnips and potatoes. Stir in the crème fraîche and 40 g butter, season with salt and pepper and add 60 g of the parmesan. Spread on the gratin dish, sprinkle with the rest of the Parmesan and lay out the remaining 20 g butter in flakes. Gratinate on the top rail of the oven for 20 minutes.