Preheat your oven to 375°F / 190°C. Grease a baking dish (approx. 23x33 cm / 9x13 inches or similar size) and set it aside.
In a large pot of salted boiling water, cook the penne pasta according to the package instructions until al dente. Drain the pasta and set aside.
In a large skillet, heat up the oil and melt the butter over medium heat. Add the chopped onion and sliced mushrooms. Cook until the onions are translucent and the mushrooms are tender, about 5-6 minutes.
Add minced garlic to the skillet and sauté for a minute until fragrant. Add the diced chicken, season with salt and pepper, and cook until the chicken is no longer pink on the outside, about 4-5 minutes.
Sprinkle the flour over the chicken and vegetables. Stir well to coat everything in the flour.
Slowly pour in the chicken broth while stirring continuously to avoid lumps. Then, pour in the heavy cream and add fresh parsley. Stir the mixture continuously and let it simmer until it slightly thickens about 5 minutes. Adjust the seasoning with salt and pepper if needed.
Turn off the heat. Add the cooked pasta to the pan and stir until the pasta is well coated with the creamy sauce. Add half of the shredded mozzarella cheese and stir shortly until melted and incorporated into the sauce.
Transfer the creamy pasta mixture to the prepared baking dish. Spread it out evenly. Sprinkle the remaining mozzarella cheese over the top.
Bake in the preheated oven for 15-20 minutes or until the cheese is bubbly and golden brown.
Remove the pasta bake from the oven and let it cool for a few minutes. Garnish with additional fresh parsley if desired. Enjoy!
