Preheat the grill to medium heat.
In a small bowl, whisk together the soy sauce, mirin, and honey.
Brush the chicken breasts and eggplant slices with the vegetable oil.
Grill the chicken breasts and eggplant slices for about 5-7 minutes per side, or until the chicken is cooked through and the eggplant is tender.
Remove the chicken and eggplant from the grill and let them rest for a few minutes.
Slice the chicken into thin strips.
To assemble the donburi bowls, divide the cooked rice between two bowls.
Top the rice with the grilled chicken and eggplant.
Drizzle the soy sauce mixture over the top of the chicken and eggplant.
Garnish with sliced green onions.
Serve hot and enjoy!