Layer the chopped onion and celery in the bottom of a large slow cooker.
Place the whole chicken on top of the vegetables.
Sprinkle the chicken with dried garlic, thyme, salt, and pepper, then add the bay leaf.
Pour in the water and dot the chicken with bits of butter.
Cover and cook on LOW for 7 to 9 hours, or until the chicken is fall-off-the-bone tender. Carefully transfer the chicken to a cutting board or tray to cool slightly.
Once cool enough to handle, shred or chop the meat, discarding the skin and bones.
Strain the cooking liquid through a fine-mesh sieve back into the slow cooker pot to create a clear broth; discard the cooked-down vegetables.
Stir the shredded chicken, sliced napa cabbage, and bok choy into the broth.
Cover and cook on HIGH for 30 to 60 minutes, just until the cabbage is tender-crisp.