In a 4- to 6-quart slow cooker, place the chicken, ginger, garlic, chicken stock, and coconut aminos. Cover and cook on HIGH for 4 hours.

Remove the chicken from the slow cooker and with 2 forks or a shredder, shred the chicken. Return the shredded chicken to the slow cooker.

In a small bowl, whisk the eggs, sesame oil, and ⅛ teaspoon of the sea salt. Whisk the egg mixture into the hot soup. Season with the remaining sea salt and black pepper.

Serve topped with the sliced green onions.