Cook the pasta: Cook the penne pasta according to package directions until al dente. Reserve about 1/2 cup of pasta water before draining.
Cook the chicken: While the pasta is cooking, heat the olive oil in a large skillet over medium-high heat. Season the chicken slices with salt and pepper. Add the chicken to the skillet and cook until browned and cooked through, about 5-7 minutes. Remove the chicken from the skillet and set aside.
Sauté vegetables: In the same skillet, melt the butter over medium heat. Add the sliced mushrooms and cook until softened and lightly browned, about 5 minutes. Add the minced garlic and cook for another minute until fragrant. Add the asparagus pieces and cook until tender-crisp, about 3-5 minutes.
Make the sauce: Pour in the chicken broth (or white wine) to deglaze the pan, scraping up any browned bits from the bottom. Let it simmer for a minute or two. Reduce heat to low, then stir in the heavy cream and Parmesan cheese. Season with salt and pepper to taste. Let the sauce simmer gently for a few minutes, allowing it to thicken slightly.
