Cook wild rice in water as directed on package.
Meanwhile, heat oven to 350°F. Grease 13x9-inch (3-quart) baking dish. In large skillet, cook onions, sausage and mushrooms over medium-high heat until sausage is no longer pink. Drain.
Combine cooked wild rice and sausage mixture in greased baking dish. With back of large spoon, make 8 evenly spaced indentations in mixture. Crack 1 egg into each indentation. Pierce egg yolks but do not stir. In small bowl, combine milk and flour; blend well. Pour over rice, avoiding eggs.
Bake at 350°F. for 30 to 40 minutes or until eggs are set. Sprinkle with cheese; bake an additional 2 to 3 minutes or until cheese is melted. Sprinkle with parsley.