Preheat the oven to 350°F (175°C).
Cook the egg noodles according to package instructions until al dente. Drain and set aside.
In a large skillet, melt the butter over medium heat. Add the diced onion and minced garlic and sauté for 3-4 minutes until softened.
Add the sliced mushrooms to the skillet and cook for an additional 5 minutes until mushrooms are tender.
In a large mixing bowl, combine the cooked egg noodles, sautéed onion, garlic, and mushrooms, shredded chicken, frozen peas, and frozen carrots.
In a separate bowl, whisk together the condensed cream of mushroom soup, sour cream, chicken broth, dried thyme, salt, and black pepper until smooth.
Pour the sauce mixture over the noodle and chicken mixture. Stir gently to combine all ingredients evenly.
Transfer the mixture into a greased 9×13 inch casserole dish and spread evenly.
Sprinkle shredded cheddar cheese and grated Parmesan cheese evenly over the top.
Bake uncovered in the preheated oven for 30-35 minutes until the casserole is bubbly and the cheese is melted and golden.
Remove from the oven and let it rest for 5 minutes before serving.