Cook the penne pasta according to package instructions until al dente. Drain and set aside.

In a large skillet, heat olive oil over medium heat. Add the diced chicken and cook until browned and cooked through, approximately 5-7 minutes. Season with salt and pepper.

Toss in the chopped asparagus and sliced mushrooms to the skillet, along with the minced garlic. Sauté for another 4-5 minutes, until the vegetables are tender.

Reduce the heat to low and pour in the heavy cream. Stir well to combine, then add the grated parmesan cheese. Allow it to simmer for 2-3 minutes, stirring until the cheese has melted and the sauce has thickened slightly.

Add the cooked penne to the skillet and toss everything together until the pasta is well-coated. Adjust seasoning if needed. Serve warm, garnished with fresh parsley if desired.