Pour the broth and water into a large pot or Dutch oven, then stir in the salt, pepper, garlic powder, and onion powder. The broth should smell savory and well seasoned as it starts to warm.
Add the chicken breasts and butter, cover the pot, and heat over medium until the liquid begins to boil. Once it reaches a boil, lower the heat and cook covered for 30 minutes so the chicken stays tender while it poaches.
Lift the chicken out and let it cool enough to handle. Resting it briefly makes it easier to shred or cut cleanly without losing as much moisture.
Shred the chicken with two forks or cut it into bite-sized pieces, then set it aside. The pieces should be tender and easy to pull apart, not rubbery.
Whisk both cans of cream of chicken soup into the hot broth until the mixture is smooth, then bring it back to a boil and add the egg noodles. Some noodles may sit above the liquid at first, but they will soften and settle as they cook.
Lower the heat to medium, cover, and cook for 3 to 5 minutes, stirring now and then. The noodles are ready for the next step when they are still too firm to eat but bend without snapping.
Stir the chicken back into the pot, turn off the heat, and keep the pot covered while it rests. After 5 to 20 minutes, the noodles finish cooking and the sauce thickens enough to cling to them.