Preheat the oven to 350 degrees F (175 degrees C).

Fill a large pot with water and bring to a simmer over medium heat. Add chicken; poach in simmering water until no longer pink in center, about 12 minutes. Use a slotted spoon to remove chicken from pot and set aside. Leave water in the pot.

Bring chicken cooking water to a boil. Stir in egg noodles and cook until tender with a slight bite, about 10 minutes. Drain.

Transfer noodles to a large bowl. Cut chicken into bite-size pieces and mix with noodles.

Mix together both condensed soups and sour cream in a separate bowl. Season with salt and pepper. Add soup mixture to chicken mixture and gently stir until combined. Transfer to a 2-quart baking dish.

Melt butter in a small saucepan over low heat and remove from heat. Stir in crumbled crackers. Sprinkle mixture over top of casserole.

Bake in the preheated oven until heated through and browned on top, about 30 minutes.