Peel the carrots, turnips and potatoes. Dice the potatoes, slice the remaining vegetables into thin slices. Chop the onion, sauté in hot oil. Add the potatoes and half of the carrots, sauté briefly. Pour in the stock, cook for approx. 6 minutes, puree finely. Stir in the crème fraîche. Chop and fold in the parsley. Season to taste with salt and pepper.
Cook the turnips and the remaining carrots in salted water for about 4 minutes until al dente, then drain.
Preheat the oven to 180 ° C top / bottom heat. Cover the bottom of a baking dish with sauce, place 4 sheets of lasagne on top. Spread some sauce on top, cover with vegetables and some cheese. Then another layer of pasta, top with sauce and cheese. Bake at 180 ° C for about 30 minutes until golden brown.