Heat half of the oil in a pot over medium heat. Add in the onion, celery, and garlic; sauté for 3-5 minutes until the vegetables start to soften. Season with salt and pepper.
Add in the broth and chicken. Cover with a lid and simmer until the chicken reaches an internal temperature of 160°F using a thermometer. Remove the chicken from the pot and set aside.
Add half of the beans to the pot, then using a whisk or fork, mash up the remaining beans and add them to the pot. Bring back to a simmer and stir in the kale.
Shred the chicken using two forks, pulling it apart in opposite directions. Add the shredded chicken back into the pot and simmer on low. Taste and adjust the seasoning with salt if needed.
Heat the remaining oil in a pan over medium heat. Add the sliced garlic and sauté until it starts to turn golden brown. Once it starts to turn golden brown remove the pan from the heat and set aside.
Ladle the soup into the bowl, spoon the garlic oil over top, garnish with celery leaves.