Preheat the oven to 350°F (175°C).
Cook the whole wheat egg noodles according to package instructions until al dente. Drain and set aside.
Heat the olive oil in a large skillet over medium heat. Add the chopped onion, celery, carrots, and mushrooms. Sauté for 5-7 minutes until vegetables are tender.
Add the minced garlic to the skillet and cook for 1 minute until fragrant.
In a large mixing bowl, combine the cooked chicken, sautéed vegetables, cooked noodles, thawed peas, Greek yogurt, chicken broth, dried thyme, dried parsley, salt, and black pepper. Mix well until all ingredients are evenly incorporated.
Transfer the mixture to a 9×13 inch casserole dish and spread evenly.
Sprinkle the grated Parmesan cheese evenly over the top of the casserole.
Bake in the preheated oven for 25-30 minutes, until the casserole is bubbly and the top is lightly golden.
Remove from the oven and let it cool for 5 minutes before serving.