For the Jerusalem artichoke puree, peel the Jerusalem artichoke tubers and the potatoes and cut them into small pieces. Boil the potatoes in salted water for 5 minutes, then add the Jerusalem artichoke pieces. Cover and cook for another 15 minutes until soft.
Meanwhile, peel the onions, cut into fine rings and fry in oil. Finely chop the parsley.
Strain the Jerusalem artichokes and potatoes, let them steam out and press them through a potato ricer. Stir butter and crème fraîche into the puree, season with pepper and salt.
Sprinkle the Jerusalem artichoke puree with parsley and fried onions before serving.