For the potato pan, cut the potatoes into eighths or other wedges. Slice or slice the onion into rings. Clean mushrooms with damp kitchen paper and cut in half if necessary. Wash and roughly dice the tomatoes. Rinse and drain the arugula.
Saute onion rings over medium heat in enough oil or clarified butter until translucent. Turn up heat, add potato wedges and saute until properly browned. Fry over medium heat, with the lid closed at best, for about 15 minutes, depending on the thickness of the potatoes. Then add the mushrooms and fry them nicely.
After a while, when the mushrooms are almost cooked, add the diced tomatoes. Again increase heat for one or two minutes.
Finally, add the arugula to the pan, salt and pepper and add the olive oil. Turn briefly and then serve the potato pan immediately hot!