Bring a pot of salted water to a boil over high heat. Add cubed potatoes; reduce heat to medium and cook until fork tender, about 15 minutes. Drain and return potatoes to the pot; set aside.
Meanwhile, in a large skillet, sauté onions, carrots, and celery in butter until onions are translucent and the vegetables are tender. Add minced garlic, stir for 1-2 minutes. Stir in flour continue stirring for 1-2 minutes.
Gradually stir in broth, and half-and-half. Cook, stirring constantly, until mixture thickens.
Season with salt, pepper, and thyme. Add left-over turkey and continue to stir until turkey is heated through.
Ladle into soup bowls. Serve with crumbled bacon and crackers.