In a large pan, sauté mushrooms, thyme and onions in oil over medium heat until tender. Add garlic and carrots, cook until the garlic becomes fragrant, about three minutes. Add broth and salt. Bring to boil, then reduce heat and simmer uncovered for ten minutes or until carrots are tender.
Meanwhile, in a large bowl whisk eggs and flour together until smooth. Crumble cooked stuffing into dough and mix well. If dough is dry, add water by one teaspoon at a time to moisten until mixture holds shape. Drop stuffing mixture by heaping tablespoons onto simmering soup. Cover and simmer for ten minutes or until toothpick inserted into dumpling comes out clean (try not to lift cover while dumplings are cooking). Remove from heat and serve.