In a large heavy-bottom pot over medium heat, melt the butter. Add the onion and sauté 3–4 minutes until soft, then add garlic and cook until fragrant, 30–45 seconds.
Pour in the chicken bone broth + water. Stir in salt, pepper, oregano, and bouillon. Add the celery and carrots.
Turn heat up just until the liquid comes to a gentle boil, then lower heat to a simmer.
In a smaller pot, cover chicken with water, bring to a gentle boil, then reduce to simmer for 15–18 min. Rest 5 minutes, shred with forks, and add back to the soup.
Let the soup gently simmer 40–60 more minutes so the broth develops richness and sweetness from the carrots and celery. Longer simmer = deeper flavor.
While the soup simmers, boil egg noodles in a separate pot according to package directions. Drain.
Add shredded chicken to the simmering broth, then adjust seasoning to taste. Serve by placing noodles in bowls first, then ladling hot soup and chicken over them.