In the stockpot over medium-high heat, heat the olive oil until hot. Add the curry paste and cook for 1 minute, stirring. Add the sweet potatoes, chicken, and broccoli, and cook for 4 minutes.
Add the coconut milk and water to the pot, and whisk until combined. Bring just to a boil, then reduce the heat, cover, and simmer gently for about 20 minutes, stirring occasionally.
Ladle the soup into bowls. Garnish with the cilantro, if using, and serve.