Spray a 9 x 13-inch pan or casserole dish with Pam.
Line the bottom with bread. Arrange cooked link sausages on top.
Sauté onion in oil over medium heat until clear, about 2 minutes. Add mushroom and sauté until limp, for 4-5 minutes.
Arrange over sausages. Whisk together eggs, milk, and soup.
Ladle over the onion mixture. Sprinkle shredded cheese evenly over the top. Cover and refrigerate overnight.
Preheat oven to 350°F.
Bake, uncovered, until heated through, about 40 minutes.
Serves 4.