Make the marinade. Heat the sesame oil until glistening in a small saucepan over medium heat. Add the ginger and garlic and cook until fragrant, about 1 minute. Add the soy sauce, rice vinegar, brown sugar, ketchup and smoked paprika, stirring to combine.
In a small bowl, mix the water and cornstarch together to make a slurry. Add the cornstarch slurry to the sauce in the pan, mixing until combined. Bring to a boil, then reduce the heat to medium low/low and simmer until the huli huli sauce is thick enough to coat the back of a wooden spoon. Remove from the heat.
Reserve 1/2 cup of the sauce for basting. Set the remaining marinade aside to cool for 5 minutes. Place the chicken in a large bowl and toss with remaining marinade. Use right away or place the chicken in the fridge to marinate for 30 minutes and up to 4 hours.
Heat a gas grill to medium high. Oil the grill racks. Using tongs, place the marinated chicken on the grill and grill for 4-6 minutes on each side. Baste the chicken with the reserved sauce, flip the chicken pieces and grill for 2-4 minutes. Baste the chicken thigh pieces again and flip them. Grill the huli huli chicken until it is cooked through. Look for an internal temperature of 165°F on an instant read thermometer.
