Heat the oven to 400°F. Lightly brush 8 cups of a standard muffin tin with 1 teaspoon of the sesame oil.
Rinse the rice under cool water. Add it to a saucepan with the water and the remaining 2 teaspoons of sesame oil. Bring to a boil, then cover and reduce the heat to low. Cook until the water is absorbed and the rice is tender, about 15 minutes. Remove from the heat and keep covered.
In a mixing bowl, combine the ground chicken, panko, egg, 2 tablespoons of the green onions, 2 tablespoons of the teriyaki sauce, and the grated ginger. Mix gently until just combined.
Divide the chicken mixture among the 8 prepared muffin cups. Shape each portion into a rounded mound, then brush the tops with the remaining teriyaki sauce.
Bake until the muffins are cooked through and the centers reach 165°F, about 20 to 25 minutes.
Fluff the rice with a fork and stir in the sesame seeds. Serve the mini meatloaves over the rice, topped with the remaining green onions.