Heat oven to 350°F and lightly grease a 9x13-inch baking dish; set a rack in the center.
In a large skillet over medium heat, melt the butter. Add the diced onion and cook until translucent and lightly softened, about 4 minutes. Stir in the minced garlic and cook 30–45 seconds until fragrant.
Reduce heat to medium-low. Whisk the cream of chicken soup, sour cream, and Dijon into the skillet and warm 2 minutes to loosen and combine. Remove from heat.
Meanwhile, bring a large pot of salted water to a boil. Cook the egg noodles 1 minute less than package directions for al dente. Drain well.
In a large mixing bowl, combine the shredded chicken and thawed peas and carrots. Add the drained noodles, then season with the salt and black pepper.
Pour the warm creamy mixture over the bowl and gently fold until everything is evenly coated. Let stand 2 minutes to thicken slightly.
Spread the mixture into the prepared baking dish. Cover loosely with foil and bake for 12 minutes. Uncover and bake 5–8 minutes more, until hot and bubbling at the edges.
Rest 5 minutes before serving. Garnish with chopped parsley, if using.