Melt butter in a stockpot over low heat. Add celery, carrots, onion; cook and stir until tender, 8 to 10 minutes. Stir in turkey, stuffing, tomatoes, and parsley. Pour in turkey stock. Bring soup to a boil; reduce heat and simmer, partially covered, until flavors combine, about 1 hour.
Bring a large pot of lightly salted water to a boil. Cook egg noodles in the boiling water, stirring occasionally until tender yet firm to the bite, 7 to 9 minutes. Drain.
Scoop hot noodles into deep serving bowls; ladle soup on top.