Cook the pasta in salted boiling water according to package directions until al dente. Reserve a splash of the pasta water, then drain and set aside.
While the pasta cooks, heat the olive oil in a large skillet over medium-high heat. Add the diced chicken, season with a pinch of salt and pepper, and cook until lightly browned and cooked through, about 5–7 minutes. Transfer the chicken to a plate.
In the same skillet, add the mushrooms. Sauté until they release their moisture and start to brown, about 5 minutes. Add the minced garlic and cook for another 30 seconds, until fragrant.
Pour in the chicken broth and bring to a gentle simmer. Scrape up any browned bits from the bottom of the pan as you go.
Stir in the heavy cream and Parmesan cheese. Let the sauce simmer for a few minutes until it thickens slightly. If it’s too thick, splash in a little reserved pasta water to loosen it.
Return the cooked chicken to the skillet and toss to coat in the sauce. Season to taste with salt and pepper.
Toss the cooked pasta into the sauce, stirring until evenly coated and glossy. If needed, add a bit more pasta water to reach your desired consistency.
Garnish with chopped parsley (if using) and serve hot. A light crack of pepper on top pairs nicely.