In a dutch oven, over medium heat, sauté the chicken pieces in 1 T olive oil until they are lightly browned, about 5 minutes. Transfer the chicken to a bowl and set aside.
Add the remaining olive oil to the dutch oven and sauté the onion, garlic and green chili over medium heat for 3 - 5 minutes or until they begin to soften.
Add the ginger and red curry paste and sauté for 1 minute.
Add the fish sauce, chicken stock, coconut milk, lime juice and honey. Mix to combine.
Add the chicken and broccolini and mix well to combine. Bring to a boil, reduce heat to low, cover and simmer for 15 minutes.
Serve over cooked rice, garnished with cilantro leaves.