Cook the pasta. Bring a large pot of salted water to a boil. Add the fettuccine and cook according to the package directions until al dente. Before draining, reserve at least ½ cup of pasta water. Drain the pasta and set it aside.
Sauté the mushrooms. Heat the olive oil and 1 tablespoon of butter in a large skillet over medium-high heat. Add the sliced mushrooms in a single layer as much as possible. Cook for 5–7 minutes, stirring occasionally, until they release their moisture and develop golden-brown edges.
Add the garlic. Reduce the heat to medium and add the remaining tablespoon of butter. Stir in the minced garlic and cook for about 30–60 seconds, until fragrant. Avoid browning the garlic, as it can become bitter.
Make the creamy sauce. Sprinkle the flour over the mushrooms and stir well to coat. Cook for about 1 minute to remove the raw flour taste. Slowly pour in the heavy cream and milk, stirring continuously to create a smooth sauce.
Season the sauce. Add the Italian seasoning, black pepper, and salt. Let the sauce simmer gently for 2–3 minutes, stirring frequently, until it begins to thicken. Keep the heat moderate and avoid a vigorous boil.
Add the Parmesan. Lower the heat and gradually stir in the freshly grated Parmesan cheese until melted and smooth. If the sauce becomes too thick, add a splash of reserved pasta water to loosen it.
Combine the pasta and sauce. Add the cooked fettuccine to the skillet and toss gently until every strand is coated. Add more pasta water, a tablespoon at a time, until the sauce reaches a silky consistency that clings to the noodles.
Garnish and serve. Remove the skillet from the heat. Sprinkle with chopped fresh parsley and additional Parmesan cheese. Serve immediately while the sauce is creamy and warm.