Heat the olive oil in a large skillet over medium-high heat; add turkey and cook for 5 minutes or until brown, turning once. Place carrots, celery, onion and garlic in a slow cooker then place turkey on top.
In a small bowl, combine broth, soy sauce and gingerroot; pour over turkey. Cover and cook on LOW for 6 to 8 hours.
In a small bowl, combine cornstarch and water and stir into turkey mixture. Stir in mushrooms and snow peas.
Raise heat setting to HIGH; cover and cook for 15 minutes. Serve.