In a 6-quart saucepan, melt butter over medium-high. Add celery, carrots, onion, and 1/2 teaspoon salt and cook until onion softens, about 3 minutes.
Add stock and bring to a rapid simmer. Add noodles, rosemary, 2 teaspoons salt, and 3/4 teaspoon pepper and simmer until noodles are tender, 10 to 12 minutes. Add turkey and heat through.