In a large pot over medium heat, melt the butter.
Add the diced onion, chopped celery, and sliced carrots to the pot. Cook, stirring occasionally, until the vegetables are just tender, about 5 to 8 minutes.
Stir in the minced garlic, dried thyme, dried rosemary, kosher salt, and ground black pepper. Cook for about 1 minute, stirring constantly, until fragrant.
Pour in the turkey broth and increase the heat to bring it to a boil.
Once boiling, add the uncooked egg noodles. Cook for about 8 minutes, or until the noodles are just tender.
Stir in the cubed cooked turkey and let it boil for another 1 to 2 minutes, or until the turkey is heated through.
Taste and adjust seasoning with additional salt and pepper, if needed. Serve hot.