Heat a large skillet over medium heat. Add the oil, followed by the leeks and celery. Cook for 4-5 minutes until soft and add the garlic. Cook for 30 seconds and add the sweet potatoes. Cook for about 2 more minutes until potatoes are slightly browned. Add the kale or spinach and the curry powder and combine until wilted. Season with salt and pepper. Transfer this mixture to your slow cooker.
Add the black beans and vegetable broth and turn the slow cooker on low heat. Cook for 2-3 hours on low. About 15-20 minutes before serving, add the brown rice, coconut milk and lime juice. Continue to cook until flavors are combined. Taste, season with more salt and pepper if desired and serve.