Place the chicken in a large pot with 14 cups water. Bring to a boil over high heat, then immediately reduce the heat to medium-low and simmer for 1 hour. Periodically skim off the foam and scum that floats to the top. Transfer the chicken to a platter to cool.
Add the carrots, fennel, onion, garlic, chiles, star anise and ginger to the stock and simmer until the garlic is fork tender, 15 to 20 minutes. Shred the chicken breast and leg meat (about 4 cups total), and add back to the soup along with the broccoli. Simmer for 5 minutes, and season with salt and pepper. Remove the chiles and ginger, and then serve the soup garnished with fennel fronds.
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