Bring a large pot of salted water to a boil; add the pasta and cook until al dente, about 9 minutes. Drain the pasta, reserving about 1/4 cup cooking water.

Meanwhile, melt 4 tablespoons butter in a large skillet over medium heat. Stir in the flour with a wooden spoon to make a paste. Cook, stirring, until the paste puffs slightly, about 1 minute.

Remove from the heat and gradually whisk in the milk until smooth. Bring to a boil over medium-high heat, whisking. Reduce the heat and simmer, whisking occasionally, until the sauce is creamy, 8 to 10 minutes. Add the nutmeg and season with salt and pepper.

Meanwhile, heat 2 tablespoons butter and the olive oil in a large skillet over medium-high heat. Add half of the mushrooms and cook until soft, about 8 minutes. Season with salt. Push to the side of the pan and repeat with the remaining mushrooms.

Reduce the heat under the sauce to low and whisk in both cheeses until smooth. Stir in the mushrooms and pasta and toss, adding the reserved cooking water as needed.

Melt the remaining 2 tablespoons butter in a skillet over medium heat. Add the breadcrumbs and toast until golden; stir in the parsley. Divide the pasta among 8 small bowls. Garnish with the breadcrumb mixture.