Cook the rice according to the instructions on the package. Once done, season with salt and pepper to taste. Cover with a lid to keep warm.
Heat a pot over medium heat. Once hot, add the oil. Sauté the garlic, pepper, onion, and ginger until the onion starts to soften.
Add the broth, lemongrass, chicken, and lime juice. Stir well, bring to a low simmer until the chicken reaches an internal temperature of 160°F using a thermometer.
Once the chicken is cooked, pull it apart using tongs into smaller bite sized shreds. Add the broccoli to the pot, simmer until tender. Season with salt and pepper to taste.
Taste and adjust the seasoning with salt and pepper as needed. Garnish with scallions. Serve with rice.