Preheat the oven to 350°F (175°C).
Cook the egg noodles according to package instructions until al dente. Drain and set aside.
Heat olive oil in a large skillet over medium heat. Add the diced onion and cook for 3-4 minutes until softened.
Add the minced garlic and sliced mushrooms to the skillet and cook for an additional 5 minutes until mushrooms are tender.
In a large mixing bowl, combine the cooked chicken, cooked egg noodles, sautéed onion, garlic, mushrooms, frozen peas, cream of mushroom soup, cream of chicken soup, sour cream, shredded cheddar cheese, chicken broth, dried thyme, black pepper, and salt. Mix well until fully combined.
Transfer the mixture to a greased 9×13 inch casserole dish and spread evenly.
In a small bowl, mix the crushed buttery crackers with the melted butter until the crumbs are evenly coated.
Sprinkle the cracker topping evenly over the casserole.
Bake uncovered in the preheated oven for 35-40 minutes, or until the casserole is bubbly and the topping is golden brown.
Remove from oven and let it rest for 5 minutes before serving.