1. Preheat your oven to 350°F (175°C) to ensure even baking and a golden top.
2. Boil salted water in a large pot, then cook the pasta until al dente (about 2 minutes less than the time stated on the package). Drain the pasta and set aside.
3. Melt 3 tablespoons of butter in a large skillet over medium heat. Add chopped onion, minced garlic, and sliced mushrooms, then sauté until the onions are translucent and mushrooms are soft (about 5-7 minutes).
4. Sprinkle 3 tablespoons of flour over the sautéed vegetables, stirring continuously for 1-2 minutes to let the flour cook slightly and act as a thickener.
5. Gradually whisk in 2 cups of milk and 1 cup of heavy cream, stirring to prevent lumps. Once combined, add 1 cup of chicken broth and 1/4 cup of sherry or white wine. Bring the sauce mixture to a simmer until slightly thickened.
6. Add the cooked, shredded chicken, frozen peas, 1/2 cup of grated Parmesan cheese, salt, and pepper to the sauce. Mix thoroughly to coat all ingredients evenly.
7. Combine the cooked pasta with the creamy sauce in the skillet, ensuring the pasta is evenly coated.
8. Transfer the pasta and sauce mixture into a greased 9×13 inch baking dish, spreading it out evenly.
9. In a separate bowl, prepare the topping by mixing 1/2 cup of breadcrumbs, the remaining 1/2 cup of Parmesan cheese, and 1 tablespoon of olive oil. Sprinkle this mixture evenly over the casserole.
10. Place the baking dish in the preheated oven and bake for 25-30 minutes, or until the top is golden brown and the casserole is heated through.
11. Remove the baking dish from the oven and let it cool for about 5 minutes to allow the sauce to set and make serving easier.
12. Serve the Chicken Tetrazzini warm and enjoy its creamy, comforting flavors with family or friends.