Preheat the oven to 375°F (190°C). Grease a medium baking dish with a little butter or oil to prevent sticking.
Cook the egg noodles in salted boiling water until just al dente, according to package instructions. Drain and set aside.
In a medium saucepan, melt the butter over medium heat. Add the onion (if using) and carrots and sauté until softened, about 3–4 minutes.
Stir in the flour to make a light roux, cooking for 1 minute to remove the raw flour taste.
Gradually whisk in the milk, then stir in the cream of chicken soup until the mixture is smooth and creamy. If you’d like a thinner sauce, add a little more milk.
Season the sauce with garlic powder (if using), thyme or parsley, and salt and pepper to taste. Let simmer gently for 2–3 minutes until slightly thickened.
Fold in the shredded chicken, peas, and half of the cheddar cheese. Remove from heat.
Combine the cooked noodles with the chicken mixture, then spoon into the prepared baking dish. Sprinkle the remaining cheddar cheese on top.
Bake for 20–25 minutes, until the casserole is bubbly and the cheese is golden. If you like a crisper top, broil for 1–2 minutes at the end, watching carefully.