Cook the pasta according to the directions on the package, adding a generous tablespoon or so of kosher salt to the water as it cooks. Drain, but do not rinse.
Melt 3 tablespoons of butter in a large skillet over medium-high heat. Add the mushrooms and cook for 3-5 minutes until browned, stirring occasionally. When the mushrooms have released their liquid, remove the pan from the heat and drain or use a paper towel to absorb the excess liquid from the pan. Return to the heat and add the garlic. Cook for about 1 minute, until fragrant. Transfer the mushrooms to a plate.
Melt the remaining 2 tablespoons of butter in a saucepan over medium heat. Whisk the flour into the melted butter and then slowly add the chicken broth, whisking to combine. Increase the heat to medium-high and bring to a simmer.
Cook for 2 minutes and then add the cream. When the sauce begins to simmer again, reduce the heat to medium and continue on a low simmer, stirring constantly for 8-10 minutes. The sauce will thicken slightly as it cooks. Season generously with salt and pepper and adjust to taste. Remove from the heat.
Return the pasta to the skillet and toss to coat. Add the mushrooms, Parmesan, and parsley. If desired, add chicken. Toss again. Serve warm.
Notes
While this pasta is absolutely delicious as a vegetarian meal, it's also terrific with the optional chicken added to it. The sauce can be made with vegetable stock or chicken stock, depending on your preference.