Arrange the chicken thighs in a 6-quart slow cooker.
Whisk the soy sauce, broth, rice vinegar, honey, ginger, garlic and sesame oil and pour it over the chicken.
Cover and cook on low until the thighs are tender and reach at least 165°F, 3 1/2 to 4 hours.
Add the broccoli over the chicken, cover and cook on high until crisp-tender, 20 to 30 minutes.
Move the chicken and broccoli to a platter and stir the cornstarch mixed with cold water into the sauce.
Cook uncovered on high until glossy, 5 to 8 minutes.
Spoon the sauce over the chicken and broccoli and serve with the hot rice.