Bring a large pot of salted water to a boil and cook egg noodles just shy of al dente, according to package directions. Drain and set aside.
While the noodles cook, add sausage and onion to a large oven-safe skillet set over medium-high heat. Cook for 4-5 minutes, stirring to break the sausage up into crumbles, until the onion is tender and the sausage is browned. Using a large spoon or spatula, transfer the mixture to a paper towel-lined plate and set aside. If a lot of fat remains in the pan, drain a bit off.
Melt butter in the same skillet, then add the chopped mushrooms and cook for 3 minutes. Stir in the flour and cook for 1 minute more. Gradually stir in milk and broth, then season with salt, pepper, and nutmeg. Bring the sauce to a simmer and cook for 3-4 minutes to thicken slightly.
Return sausage and onion to the pan, followed by the cheese and cooked egg noodles. Stir well and remove pan from the heat. Sprinkle breadcrumbs evenly on top.
Transfer skillet to the oven and bake for 20 minutes. Remove from the oven, serve, and enjoy!
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Notes
This makes a large casserole. Leftovers keep very well, so it's great for sharing or eating over several days. Of course you can also halve the recipe; I just find it simpler to use the full packages of egg noodles and sausage. The extras always seem to disappear!