For the potato polenta, cook the potatoes, peel while still hot and press through the potato press. Mix with polenta flour and stir into 1 liter of hot salted water. Add olive oil, stir well and bring to a boil. Simmer gently over low heat for about 20 minutes.
In the meantime, keep stirring. Then let the polenta simmer for another 10 minutes in a warm place, covered. Form dumplings with two spoons and serve. Sprinkle the potato polenta with grated Parmesan cheese and pour brown butter over it.