Begin by bringing a large pot of salted water to a rolling boil over high heat. Add the penne pasta and cook until al dente, about 10-12 minutes. Reserve 1/2 cup of pasta water, then drain, and set the pasta aside.

Season the chicken breasts with salt and black pepper. Heat olive oil in a skillet over medium heat and cook the chicken for about 5-7 minutes on each side until golden brown. Remove and let it rest.

In the same skillet, add sliced mushrooms and minced garlic. Sauté for about 5 minutes until golden brown. Then, add asparagus and cook for another 3-4 minutes.

Slice the rested chicken into bite-sized pieces and return to the skillet. Pour in the heavy cream, and let it simmer for 2-3 minutes until thickened.

Add the cooked penne to the skillet and toss to coat in the creamy sauce. Adjust the consistency with reserved pasta water if necessary.

Stir in the grated Parmesan cheese until melted, adjusting seasoning with salt and black pepper as needed. Garnish with fresh parsley before serving.