Place the chicken breast in a steamer basket over boiling water. Add the ginger slices to the steaming water for subtle flavour. Steam for 18–20 minutes until completely cooked through with no pink remaining. Remove, let rest for 5 minutes, then shred into thin strips using two forks. Set aside.
Rinse the white rice under cold water until the water runs clear. Add the rinsed rice, water, and chicken broth to a medium saucepan. Bring to a boil over medium-high heat, then reduce to the lowest possible heat. Cook uncovered for 30–35 minutes, stirring occasionally, until the rice has completely broken down into a thick, creamy porridge. Stir more frequently towards the end — okayu thickens quickly and can catch on the bottom.
Stir the grated ginger into the okayu and cook for another 2 minutes. The porridge should be smooth, creamy, and thick enough to coat the back of a spoon. If too thick, add a splash of warm water and stir.
Divide the okayu between two bowls. Arrange the shredded chicken on top. Drizzle a few drops of sesame oil over each bowl, scatter the spring onion greens and sesame seeds over the top. Serve immediately while hot.