Begin by bringing a large pot of salted water to a boil. Add the spaghetti and cook until al dente, about 8-10 minutes. Drain and set aside.

In a large skillet, heat the olive oil over medium heat. Add the sliced mushrooms and minced garlic, and sauté until the mushrooms are tender, about 5 minutes.

Pour in the chicken broth and heavy cream, stirring well to combine. Let the mixture simmer for about 5 minutes. Season with salt, pepper, and thyme.

In a large mixing bowl, combine the cooked pasta, chicken, frozen peas, and half of the shredded cheese. Pour the creamy sauce over this mixture, stirring until everything is well coated.

Preheat your oven to 350°F (175°C). Transfer the pasta mixture into a greased 9×13-inch baking dish. Sprinkle the remaining cheese and Parmesan cheese on top.

Bake the casserole for 25-30 minutes or until the cheese is bubbly and golden. For a crispy top, you can broil it for a minute or two at the end.

Once cooled a tad, sprinkle the casserole with fresh parsley if desired. Serve warm, and enjoy!