Cook the pasta: Cook the penne pasta according to the package instructions until al dente. Drain and set aside.
Cook the chicken: In a large skillet, heat 1 tbsp olive oil over medium-high heat. Season the chicken with salt and pepper, then cook until golden brown and cooked through. Remove from the skillet and set aside.
Cook the vegetables: In the same skillet, add the remaining 1 tbsp olive oil. Sauté the mushrooms and asparagus until tender, about 5-7 minutes. Add the garlic and cook for 1 minute, or until fragrant.
Make the sauce: Stir in the heavy cream, chicken broth, Parmesan cheese, and thyme. Bring to a simmer and cook until the sauce thickens slightly.
Combine and serve: Add the cooked pasta and chicken to the skillet. Toss to coat everything in the sauce. Garnish with fresh parsley, if desired, and serve hot.
