In a large Dutch oven, heat olive oil over medium heat.
Add onions, carrots, and celery and cook until vegetables begin to soften, about 5-6 minutes.
Add garlic and cook until fragrant, about 30-60 seconds.
Add dried thyme, bay leaf, salt, and pepper. Stir to combine.
Pour in chicken broth and the beans. Bring to a simmer, then add the shredded turkey. Simmer for 15-20 minutes to allow flavors to meld.
Add chopped kale and cook until just wilted but still bright green, about 2-3 minutes.
Taste and adjust seasonings as needed, then serve.