Best Chicken Noodle Casserole

12 oz. wide egg noodles
2 (10.5-oz.) cans cream of chicken soup
1 cup whole milk
1 cup shredded sharp cheddar cheese
1 tsp. ground black pepper
1/2 tsp. kosher salt
3 cups cooked, shredded chicken (from 1 rotisserie chicken)
1/2 small yellow onion, finely chopped
2 celery stalks, finely chopped
1 (12-oz.) bag frozen peas and carrots, thawed
1 1/2 cups coarsely crushed butter crackers (such as Ritz, about 1 cracker sleeve)
2 Tbsp. unsalted butter, melted
Chopped parsley, to serve

Preheat the oven to 375°F. Bring a large pot of salted water to a boil over medium-high. Add the egg noodles and cook, stirring occasionally, until just al dente, about 7 minutes. Drain and set aside.

Stir together the cream of chicken soup, milk, cheese, pepper, and salt in a large bowl. Stir in the chicken, onion, celery, peas, and carrots. Gently fold in the egg noodles. Transfer mixture to a 13-by-9-inch baking dish and spread in an even layer.

Stir together the cracker crumbs and butter in a medium bowl. Sprinkle mixture evenly over the casserole. Bake until heated through and the topping is lightly browned, 30 to 35 minutes. Sprinkle with parsley and serve.