Drain and rinse the jackfruit and cut it into thin slices. Transfer the slices to a bowl and add the tamari, white pepper, and nutritional yeast. Stir to combine and set aside.
Heat 1 tablespoon of olive oil in a pot over low heat.
Add the garlic, onion, celery, carrot, bay leaves, and thyme. Saute for 5 minutes.
Add 2 tablespoons of water. Cover and cook for 5 minutes until the vegetables are tender.
Add the remaining tablespoon of olive oil to a skillet and heat over medium heat.
Add the jackfruit and cook for 3 to 5 minutes, gently pulling it apart with a fork as you cook.
Stir the jackfruit into the pot. Add the lemon zest, vegetable stock, and water. Bring the soup to a boil.
Reduce the heat and simmer the soup for 20 minutes.
Add the broken spaghetti and cook until the pasta is al dente.
Take out the bay leaves and thyme.
Stir in the baby spinach to the soup. Season with salt to taste.