In a small bowl, whisk together the soy sauce, honey, rice vinegar, minced garlic, and grated ginger until the honey dissolves.
Place the chicken thighs in the slow cooker and pour the sauce mixture over them. Add the broccoli florets, sliced red bell pepper, and shredded carrots on top of the chicken.
Cover and cook on low for 6 hours or until the chicken reaches an internal temperature of 165 degrees.
Remove the chicken from the slow cooker and shred it with two forks. Return the shredded chicken to the slow cooker and stir everything together so the vegetables and chicken coat evenly in the sauce.
Spoon the cooked rice into four bowls. Top each bowl with a portion of the chicken and vegetable mixture.
Sprinkle the sliced green onions and sesame seeds over each bowl before serving.