Place the chicken thighs in the bottom of the slow cooker.
Stir together the soy sauce, honey, rice vinegar, garlic, and ginger in a small bowl until the honey dissolves. Pour the mixture over the chicken.
Cover and cook on low for 6 hours or on high for 3 hours until the chicken is tender.
Remove the chicken to a plate and keep it warm. Pour the cooking liquid into a small saucepan. Mix the cornstarch with 2 tablespoons of water, then stir it into the liquid. Simmer for 2 to 3 minutes until the sauce thickens.
While the sauce thickens, cook the rice in a medium pot according to package directions.
Steam the broccoli florets over boiling water for 4 to 5 minutes until bright green and crisp-tender.
Serve the chicken over the rice with broccoli on the side. Spoon the thickened sauce over the chicken and finish with green onions and sesame seeds.