Heat olive oil in a large pot over medium heat. Add turkey and cook until browned.
Add onion, carrots, and celery. Cook until vegetables are softened.
Pour in chicken broth, thyme, rosemary, salt, and pepper. Bring to a boil, then reduce heat and simmer for 45 minutes.
In a mixing bowl, combine flour, baking powder, and salt for the dumplings. Cut in butter until mixture resembles coarse crumbs. Stir in milk to form a dough.
Drop spoonfuls of dough onto the simmering stew. Cover and cook for another 15 minutes, until dumplings are cooked through.
Notes:
For a richer flavor, you can use turkey thighs instead of breast.