Melt butter in a saucepan over medium heat. Add mushrooms, green onions, garlic and rosemary. Cook for 2 to 3 minutes. Sprinkle flour over mushroom mixture while stirring. Continue to stir for 3 to 5 minutes more to thicken and cook flour taste out. Add chicken stock, a little at a time while stirring. Stir in milk and sherry. Heat until almost boiling, stirring often. Remove from heat, and season with salt and pepper.
Preheat oven to 350 degrees. Brown sausage and venison in a large skillet over medium heat. While cooking, break up sausage, and mix well with venison. Add onions and carrots. Cook for 4 minutes. Stir in green beans and corn, and cook for 1 minute.
Transfer contents of skillet into a buttered 9-by-13-inch baking dish. Pour cream of mushroom soup over. In a bowl, season shredded potatoes with salt and pepper, and toss with breadcrumbs and cheese. Spread potato and cheese mixture over top.
Place in the preheated oven for 30 to 40 minutes or until cheese and potatoes are lightly browned. Allow to cool and set up for a few minutes before serving.