Coat a large stockpot with a little bit of olive oil and heat over medium-high heat.
When pot is hot enough, add the turkey in a single layer and cook over medium high heat until the pieces are nice and golden brown on all sides.
Add the onions, garlic, celery, carrots, salt and pepper and cook until fragrant and onions start to take a slight brown coloration, about 2-3 minutes.
Add turkey stock and bring the the boil. Lower heat to medium and continue cooking until the carrots are almost done but still slightly undercooked.
Bring the heat back up and when the soup starts to boil vigorously, throw in the soba noodles and cook until noodles have reached the desired level of doneness.
Remove from heat and add spinach leaves. They will wilt almost instantly.
Give the soup a quick and final stir and serve.
Notes
*Mayo Clinic has an excellent recipe for low fat chicken stock. Use the same method to make turkey stock using a turkey carcass instead of chicken bones.