Bring a large pot of salted water to a boil. Add the penne and cook according to package instructions until al dente. Reserve ½ cup of pasta water, then drain the pasta and set aside.
Heat 1 tablespoon of olive oil in a large skillet over medium-high heat. Season the chicken pieces with salt and pepper, then add them to the skillet. Cook for 5–7 minutes, stirring occasionally, until golden brown and cooked through. Remove the chicken from the skillet and set aside.
In the same skillet, heat the remaining 1 tablespoon of olive oil and the butter over medium heat. Add the sliced mushrooms and cook for 5–6 minutes, until they release their moisture and turn golden brown. Stir in the asparagus and cook for an additional 3–4 minutes, until tender-crisp. Add the minced garlic and sauté for 30 seconds to 1 minute, until fragrant.
Pour in the chicken broth and heavy cream, stirring to combine. Bring the mixture to a gentle simmer. Stir in the grated Parmesan cheese until melted and the sauce thickens slightly. If the sauce is too thick, loosen it with a splash of reserved pasta water.
Return the cooked chicken and drained pasta to the skillet, tossing gently to coat everything in the creamy sauce. Taste and adjust seasoning with additional salt, pepper, or red pepper flakes, if desired.
Transfer the pasta to serving plates or a large bowl. Garnish with fresh parsley and extra Parmesan cheese, if desired. Serve hot and enjoy the creamy, comforting goodness!
