Bring a large pot of salted water to a boil. Add the penne pasta and cook according to package instructions until al dente, about 10-12 minutes. Drain and set aside.

Season chicken breasts with salt and pepper. Heat olive oil in a skillet over medium-high heat. Cook chicken for 6-7 minutes on each side until golden brown and cooked through. Remove and let rest.

In the same skillet, add sliced mushrooms and minced garlic. Sauté over medium heat for about 4-5 minutes until mushrooms are tender and garlic is fragrant.

Add trimmed and chopped asparagus to the skillet. Sauté for an additional 3-4 minutes until bright green and tender-crisp.

Return cooked chicken to the skillet. Pour in heavy cream, stir and let simmer for about 3-5 minutes until the sauce thickens slightly.

Add cooked penne pasta to the skillet and toss everything together gently. Cook for an additional 2 minutes to heat through.

Sprinkle grated Parmesan cheese over the pasta, stirring until melted. Adjust seasoning with salt and pepper if needed.

Plate the dish and garnish with freshly chopped parsley. Serve immediately.