Pour 1 inch of water into a large pot and bring it toward a boil over medium-high heat. Put a steaming rack inside the pot, keeping the rack above the water.
Arrange the chicken in a heatproof dish. Pour the soy sauce and mirin over it.
Add the ginger and the white parts of the green onions.
When the water boils, put the dish on the steaming rack and cover the pot.
Reduce the heat so the water simmers gently. Steam for about 15 minutes, or until the thickest part of the chicken reaches at least 165°F (74°C).
Top with the green parts of the onions and serve.