Cook the pasta. Bring a large pot of salted water to a boil. Add the pasta and cook according to the package instructions until al dente. Before draining, reserve about ½ cup of pasta water. Drain the pasta and set it aside.
Sauté the garlic. Melt the butter in a large skillet over medium-low heat. Add the minced garlic and cook for 30–60 seconds, stirring frequently, until fragrant. Keep the heat moderate to prevent the garlic from browning or burning.
Make the sauce base. Sprinkle the flour over the garlic and butter. Stir continuously for about 1 minute to cook out the raw flour taste.
Add the cream and milk. Slowly pour in the heavy cream and milk, whisking as you go to keep the sauce smooth. Add the Italian seasoning, black pepper, and salt. Let the sauce simmer gently for 3–5 minutes, stirring occasionally, until it begins to thicken.
Stir in the Parmesan. Reduce the heat to low and gradually add the freshly grated Parmesan cheese, stirring until melted and smooth. Avoid boiling the sauce once the cheese has been added, as high heat can make it grainy.
Combine with the pasta. Add the drained pasta to the skillet and toss until every strand is coated in the creamy garlic Parmesan sauce. If the sauce is too thick, add a splash of reserved pasta water until it reaches your preferred consistency.
Finish and serve. Taste and adjust the seasoning as needed. Sprinkle with fresh parsley and extra grated Parmesan cheese. Serve immediately while the sauce is warm and silky.