Put the 1 lb chicken breast, diced celery, diced carrots, 3 bay leaves and ½ tsp dried thyme into a large stockpot or Dutch oven. Add 12 cups chicken broth (or water with 2 tbsp Vegeta Seasoning). Bring to a boil over medium-high heat.
Reduce heat to maintain a gentle simmer, partially cover, and cook until the chicken is cooked through and the vegetables are tender, about 20–30 minutes.
Use a slotted spoon or tongs to remove the chicken to a cutting board. Discard the bay leaves. Shred or dice the chicken and set aside.
Increase heat to bring the soup back to a gentle boil. Add the 6 oz egg noodles and cook until the noodles are tender, about 6–8 minutes (follow the noodle package if different).
While the noodles are cooking, whisk the 4 egg yolks in a heatproof bowl until smooth. Ladle 1 cup of hot broth from the pot into the bowl and whisk to temper the yolks; then ladle in a second cup of hot broth and whisk again.
Reduce the heat to low. Slowly pour the tempered egg yolk mixture into the pot while stirring constantly. Do not let the soup boil; heat gently for 1–2 minutes until the soup is warmed through and slightly thickened.
Return the shredded chicken to the pot, stir to combine, heat for 1–2 minutes more, taste and adjust seasoning as desired, and serve.