In a small bowl, stir sugar and salt into the rice vinegar to dissolve. Microwave for about 30 seconds if needed.
Cook rice according to package instructions in rice cooker or on stove. Immediately when cooked and while still hot, fold in rice vinegar with sugar and salt, diced bok choy, green onions, and sesame oil. Oil a 9x13 inch pan and add rice in an even layer. Top with sesame seeds. Once room temperature, refrigerate until firm, about 2 hours.
Once the rice is firm, use a 1 1/2 inch round cutter to cut out about 25 rice cakes. Remove excess rice and refrigerate rice cakes until ready to serve.
Thinly slice the chicken breasts 1/4 inch thick. Cut the slices into 1 inch pieces.
In a small bowl, combine hoisin, brown sugar, sake, soy sauce, chili sauce, and minced garlic.
In a large wok or pan, drizzle vegetable oil over medium high heat. Once thoroughly heated, fry the chicken until lightly browned and cooked through. Remove chicken from pan. Add the hoisin sauce mixture and bring to a boil. Reduce heat to medium and cook until sauce is thickened and reduced by half. Add the chicken and toss to coat. Remove from heat and stir in sesame oil.
Place chicken pieces over rice cakes and top with shredded green onion.