Make the sauce base. In a small bowl, whisk soy sauce, water, honey, rice vinegar, sesame oil, garlic, and ginger. In a separate small bowl, mix cornstarch with water to make a slurry.
Cook the chicken. Season chicken with salt and pepper. Heat oil in a large skillet over medium-high heat. Add chicken and cook 4 to 6 minutes per side (or until cooked through). Remove to a cutting board and slice.
Cook the veggies. In the same skillet, add broccoli and bell pepper with a splash of water. Sauté 3 to 5 minutes until crisp-tender.
Thicken the sauce. Pour sauce base into the skillet and bring to a gentle simmer. Stir in cornstarch slurry and cook 30 to 60 seconds until glossy and thickened.
Combine. Add sliced chicken back to the pan and toss to coat. If sauce is too thick, add a splash of water.
Build bowls. Serve over rice with veggies. Top with green onions and sesame seeds.