In a large bowl, whisk together soy sauce, pineapple juice, brown sugar, garlic, ginger, and sesame oil.
Add the chicken breasts and coat evenly. Cover and refrigerate for at least 2 hours or up to 6 hours.
In a small saucepan, combine soy sauce, pineapple juice, brown sugar, honey, and garlic. Bring to a gentle simmer.
Mix cornstarch and water in a small bowl. Add to the saucepan and whisk until the glaze becomes thick and glossy. Set aside.
Preheat a grill or grill pan to medium-high heat.
Grill the pineapple rings for 2–3 minutes per side until lightly caramelized. Remove and set aside.
Remove the chicken from the marinade and discard the remaining marinade.
Grill the chicken for 5–6 minutes per side or until the internal temperature reaches 165°F.
During the last 2 minutes of cooking, brush the chicken generously with the soy ginger glaze.
Let the chicken rest for 5 minutes before slicing.
Divide the jasmine rice among serving plates. Top with sliced chicken, grilled pineapple, broccoli, and bell peppers.
Drizzle with additional glaze and garnish with green onions and sesame seeds before serving.