Drain and rinse the jackfruit and cut each one into thin slices. Put into a bowl along with the tamari, pepper, and nutritional yeast. Stir to combine and set aside.
Add 1 Tablespoon of the olive oil to a large soup pot and heat over low heat. Add the garlic, onion, celery, carrot, bay leaves, and thyme. Saute for 5 minutes.
Add 2 Tablespoons of water and cook covered for around 5 minutes, until the vegetables are tender.
Meanwhile, add the second Tablespoon of olive oil to a skillet and heat over medium heat. Add the jackfruit and saute for 5 minutes, pulling it apart gently with a fork as you cook. Stir the jackfruit into the vegetables.
Add the lemon zest, stock, and remaining water. Bring the soup to a boil. Reduce the heat and simmer for 20 minutes.
Add the broken spaghetti, cooking for another 7 minutes. Remove the bay leaves and thyme, stir in the baby spinach, and season with sea salt.