Bring a large pot of salted water to a boil. Add potatoes and cook until tender but still firm, about 15 minutes. Drain and mash. Mix in butter salt, pepper and 1/4 cup shredded cheese.
Heat oil in a large frying pan. Add onion, carrots and mushrooms and cook until tender. Add ground beef and cook until well browned. Stir in flour and cook 1 minute. Add wine and beef broth. Bring to a boil, reduce heat and simmer for 5 minutes. Toss in peas and mix well.
Spread the ground beef in an even layer on the bottom of a 2 quart casserole dish. Top with the mashed potato mixture and sprinkle with remaining shredded cheese.
Bake in the preheated oven for 20 minutes, or until golden brown.