If you purchased whole mushrooms, clean and slice them.
Cook:
Cook the pasta following the instructions on the box. When the pasta is ready, reserve a cup of the pasta water, drain it, and return the pasta to the pot.
While the pasta cooks, sauté the mushrooms in a large skillet over medium-high heat. Melt 2 tablespoons of butter in the skillet and add the minced garlic and mushrooms. Sauté for about 10 minutes, until the mushrooms are soft and have turned a rich, deep brown color.
Add the remaining 4 tablespoons of butter to the pan, and the warmed heavy cream and milk. Stir to combine, scraping any bits at the bottom of the pan. Add the Parmesan cheese, salt, and pepper, and slowly stir to combine.
Reduce the heat to medium-low and simmer the Alfredo sauce for 5 minutes to reduce it.
Combine:
Add the pasta to the mushroom Alfredo sauce skillet, and using kitchen tongs, toss to combine. The sauce will be thick. Slowly add some of the reserved pasta water to the skillet to thin out the sauce to your liking.