preheat oven to 425
Melt 1 TBLS of butter in a 10 cast iron pan. Slice the onion and add to the butter with the sugar. Cover and cook until onion is softened (about 10 minutes). Remove cover and cook until onion is golden brown (about 5 mintues). Set aside.
In same skillet, melt remaining 2 TBLS of butter. Cook mushrooms until tender (5-6 minutes). set aside.
Peel potatoes (they should be russett potatoes) and cunt into 1/2 dice. Put potatoes in the skillet and toss with olive oil, rosemary, salt and pepper. Put skillet into the oven and roast till the potatoes are golden brown and tender (about 35 minutes). Remove from the oven and spread with the onions and mushrooms. Sprinkle with the grated cheese and return to the oven. Cook till cheese is melted (maybe 10 minutes)...