Place chicken breast and chicken broth into a 3-quart slow cooker. Cover and cook on Low until chicken begins to shred and is no longer pink in the center, about 4 hours. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C). Shred using 2 forks. Pour in coconut milk.

Preheat the oven to 450 degrees F (230 degrees C).

Place butternut squash face-down in a baking dish filled with 1/4 inch water.

Roast squash in the preheated oven until tender, about 30 minutes.

While squash roasts, heat sesame oil over medium heat in a saucepan. Add zucchini, celery, and green onions. Cook for 2 minutes; add lime juice, soy sauce, and ginger. Cook, stirring frequently, until zucchini and celery are soft but not mushy, about 2 minutes. Pour mixture into the slow cooker and stir to combine. Season with cayenne pepper.

Remove squash from the oven and let cool 10 minutes. Slice halves into 1-inch strips. Cut squash flesh into 1-inch cubes, making sure not to cut through skin. Remove cubed flesh with a spoon and add to the slow cooker.

Cover and cook on Low until squash has completely cooked down and flavors have melded, at least 1 hour.