Preheat oven to 350°F.
Bring a large pot of water to a boil, add a generous pinch of salt, and cook egg noodles 1 or 2 minutes shy of al dente, according to package directions. Drain and set aside.
12 ounces egg noodles
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 or dab a bit off.
1 (16 ounce) package pork sausage, 1/2 medium yellow onion
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. (It's going to look a bit odd at this stage; don't worry, it will smooth out into a nice sauce in the next step.)
4 Tablespoons butter, 1 cup mushrooms, 1/2 cup all-purpose flour
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.
1 cup milk, 1 and 1/2 cups low-sodium chicken broth, 1/2 teaspoon table salt, 8-10 cranks freshly-ground black pepper, 1/4 teaspoon ground nutmeg
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.
1 cup shredded cheddar cheese, 2/3 cup breadcrumbs
Transfer skillet to the oven and bake for 20 minutes. Remove from the oven, serve, and enjoy!