Melt the butter in a large stock pot over medium-high heat, then add your diced celery and carrots. Let them cook for about 3 minutes until they start to soften slightly. Stir in the minced garlic and cook for just 30 more seconds so it doesn't burn.
Pour in the chicken stock and stir in the salt, pepper, rosemary, thyme, and red pepper flakes. Always taste the broth at this point before adding more salt, since every stock brand varies in sodium. If it needs more depth, stir in a spoonful of chicken bouillon paste.
Bring the broth up to a full boil over high heat. Add your noodles, whether homemade or store-bought, and cook just until they turn al dente. Keep a close eye on store-bought noodles since they overcook fast and turn mushy.
Stir in your shredded rotisserie chicken once the noodles are done cooking. Give the broth one more taste and adjust the seasoning if it needs a bit more salt or herbs. The chicken just needs to warm through since it's already cooked.
Remove the pot from heat as soon as everything is combined, since noodles keep cooking even off the burner. Let the soup sit for a minute or two before ladling it into bowls. Serve it hot alongside your favorite crusty bread.