Preheat oven to 375°F (190°C). Grease a 9x13-inch baking dish.
Cook pasta according to package directions until al dente; drain and set aside.
In a large skillet, heat olive oil over medium-high heat. Add chicken and cook until golden and cooked through, about 5-7 minutes. Remove chicken and set aside.
In the same skillet, add onion and garlic; cook until softened, about 3 minutes. Add mushrooms, oregano, and thyme; cook until mushrooms are tender, about 5 minutes.
Sprinkle flour over the vegetables and stir for 1 minute. Gradually whisk in chicken broth, then add diced tomatoes. Bring to a simmer and cook until thickened, about 5 minutes.
Stir in heavy cream, then return chicken to the sauce. Season with salt and pepper. Remove from heat.
Combine cooked pasta with the sauce and transfer to the prepared baking dish. Top with mozzarella and Parmesan cheeses.
Bake for 20-25 minutes until bubbly and golden. Let rest 5 minutes before serving. Garnish with parsley if desired.
Tips
For a lighter version, substitute half-and-half for heavy cream.
This dish can be assembled ahead and refrigerated; add 10 minutes to baking time.
Leftovers keep well in the refrigerator for up to 3 days.