Bring a large pot of salted water to a boil. Add the penne pasta and cook according to package instructions until al dente—usually around 10 to 12 minutes. Drain the pasta and set aside, reserving about 1/2 cup of pasta water in case you want to loosen the sauce later.
While the pasta cooks, heat 2 tablespoons of olive oil in a large skillet over medium-high heat. Add the chopped chicken breast pieces, season with salt and pepper, and cook until browned and cooked through, about 5 to 7 minutes. Remove the chicken from the pan and set aside.
In the same skillet, add the sliced mushrooms. Sauté for 4 to 5 minutes until they release their moisture and start to brown. Add the minced garlic and cook for another minute until fragrant, stirring frequently to avoid burning.
Reduce the heat to medium and pour in 1 cup of chicken broth, scraping up any browned bits from the bottom of the pan. Let it simmer for 2 minutes, then stir in 1 cup of heavy cream. Allow the mixture to simmer gently for 3 to 4 minutes until it thickens slightly.
Stir in the grated Parmesan cheese until melted and smooth. Return the cooked chicken to the skillet, mixing everything together. Add the drained penne pasta to the pan and toss to coat fully in the creamy sauce. If the sauce feels too thick, add a splash of the reserved pasta water to loosen it.
Taste and adjust seasoning with salt and pepper as needed. Sprinkle freshly chopped parsley over the top for a burst of color and freshness. Serve immediately while warm and enjoy!