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 olive oil in a large skillet over medium heat. Add the chopped onion and cook for 3-4 minutes until softened.
Add the minced garlic, sliced mushrooms, chopped broccoli, and diced carrots to the skillet. Cook for 5-6 minutes until vegetables are tender.
Sprinkle the flour over the vegetables and stir well to coat. Cook for 1 minute to remove the raw flour taste.
Gradually pour in the chicken broth and fat free milk while stirring continuously to avoid lumps. Cook for 3-4 minutes until the sauce thickens.
Remove the skillet from heat and stir in the fat free Greek yogurt, dried thyme, dried parsley, black pepper, and salt until well combined.
In a large mixing bowl, combine the shredded cooked chicken, cooked noodles, and the creamy vegetable sauce. Mix gently to combine.
Transfer the mixture into a lightly greased 9×13 inch casserole dish. Sprinkle the shredded reduced fat cheddar cheese evenly on top.
Bake uncovered in the preheated oven for 20-25 minutes until the casserole is heated through and the cheese is melted.
Remove from the oven and let it rest for 5 minutes before serving.