Set a large sauce pot over medium heat. Add the olive oil and brown chicken thighs. Once brown put aside.
Add one tbsp olive oil and chopped onions, mushrooms, celery, ginger, and garlic. Saute for 5-6 minutes to soften. Then add broth, chicken, carrots, chopped potatoes, apple cider vinegar, turmeric, bay leaf, and 1 teaspoon sea salt.
Bring to a boil, lower the heat, and simmer for 20-30 minutes.
Remove the chicken and set aside to cool.
Add the broccoli and simmer to soften the broccoli. Meanwhile, shred the chicken with two forks, and stir it back into the soup. Once the broccoli is tender, taste, then salt and pepper as needed. Squeeze lime juice on top and serve warm.