In a large enameled stock pot over medium-high heat, melt the butter. Stir in the diced celery and carrots, sautéing for approximately 3 minutes until slightly softened. Incorporate the minced garlic and cook for an additional 30 seconds, allowing the aroma to develop.
Pour in the chicken stock and season the liquid with salt, pepper, rosemary, thyme, and crushed red pepper flakes. Sample the broth and adjust seasoning as needed, incorporating the chicken bouillon for added depth of flavor.
Increase the heat to bring the broth to a rolling boil. Stir in the noodles — whether uncooked homemade or store-bought dry pasta — and cook until just al dente. Be vigilant if using dry pasta to prevent overcooking, as the residual heat will continue to cook the noodles after removing from the burner.
Withdraw the pot from the heat source and fold in the rotisserie chicken. Conduct a final taste test and make seasoning adjustments if necessary.
Store any leftovers in an airtight container in the refrigerator for up to 4–5 days, contingent on the initial freshness of the chicken used.