Bring a large pot of salted water to a boil. Add the penne pasta and cook until al dente according to package instructions (usually about 10-11 minutes). Drain well and set aside.
Heat 2 tablespoons of olive oil in a large skillet over medium-high heat. Season the bite-sized chicken pieces with salt and pepper. Add them to the skillet and cook until golden brown and cooked through, about 5-7 minutes. Remove the chicken from the pan and set aside.
In the same skillet, add the sliced cremini mushrooms and sauté until they release their juices and become tender, roughly 5 minutes. Add the minced garlic and cook for another 1-2 minutes until fragrant.
Pour in the chicken broth and stir, scraping up any browned bits from the bottom of the skillet. Add the heavy cream, dried thyme, and half of the grated Parmesan cheese. Simmer gently until the sauce thickens slightly, about 5 minutes.
Return the cooked chicken to the skillet and stir to coat it in the creamy mushroom sauce. Add the cooked penne pasta and toss everything together until evenly mixed.
Preheat your oven to 375°F (190°C). Transfer the pasta mixture to a greased baking dish. Sprinkle the shredded mozzarella cheese on top. Bake uncovered for 20-25 minutes until the cheese is melted, bubbly, and golden.
Remove the pasta from the oven and let it rest for a few minutes. Sprinkle freshly chopped parsley over the top for a fresh, vibrant finish. Serve hot and enjoy!