Mushroom Broccoli Pasta

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. Just before the noodles are done cooking, add the broccoli to the pot. Let the broccoli boil for about 30 seconds and then drain everything into a large colander. Do not rinse the pasta.
In the same pot used to cook the pasta, melt 2 tablespoons of butter over medium-high heat. Add the mushrooms and cook for 3-5 minutes until browned, stirring frequently. When the mushrooms have released their liquid, remove the pot from the heat. Transfer the mushrooms to a bowl lined with several paper towels to absorb the excess liquid.
Melt the remaining 2 tablespoons of butter in the pot over medium heat. Whisk the flour into the melted butter and then slowly add the chicken broth, whisking constantly to combine. Increase the heat to medium-high and bring to a simmer.
Cook for 2 minutes and then add the cream, garlic, Italian seasonings, salt, and pepper. When the sauce begins to simmer again, reduce the heat to medium and continue on a low simmer, stirring constantly for 3-5 minutes. The sauce will thicken slightly as it cooks. Taste and adjust to taste. Remove from the heat after it has thickened.
Return the pasta, broccoli, and mushrooms to the pot and toss to coat. If desired, add chicken and toss again. Serve warm topped with Parmesan and parsley.