Preheat your oven to 350°F (175°C).
Cook the pasta according to package instructions until al dente. Drain and set aside.
In a large skillet, heat the olive oil over medium heat. Add the diced onion and sauté until translucent, about 5 minutes.
Add the minced garlic and sliced mushrooms. Continue to sauté for an additional 5-7 minutes, until the mushrooms are softened.
Sprinkle the flour over the vegetable mixture and stir for 1-2 minutes to cook the flour lightly.
Gradually whisk in the chicken broth, ensuring there are no lumps. Allow the mixture to simmer for 5 minutes, stirring frequently until thickened.
Stir in the heavy cream, Parmesan cheese, cooked chicken, thawed peas, dried thyme, salt, and pepper.
Combine the cooked pasta with the sauce mixture, ensuring the noodles are well-coated.
Transfer the mixture into a greased baking dish, smoothing the top with a spatula.
Sprinkle additional Parmesan cheese on top for a cheesy crust.
Bake in the preheated oven for 25-30 minutes, until bubbly and golden brown on top.
Let the dish cool for a few minutes before serving. Garnish with fresh herbs if desired.