Make the sauce: In a bowl, whisk soy sauce, water or broth, brown sugar or honey, rice vinegar, garlic, ginger, sesame oil, and red pepper flakes if using.
Load the crockpot: Place chicken in the slow cooker.
Pour the sauce over the top, making sure the chicken is mostly covered.
Cook low and slow: Cover and cook on Low for 4–5 hours or on High for 2.5–3.5 hours, until the chicken is cooked through and tender.
Steam the broccoli: About 20 minutes before serving, steam the broccoli until crisp-tender. You can also microwave it with a splash of water for 2–3 minutes. This keeps it bright and not soggy.
Thicken the sauce: Remove the chicken to a plate and shred or slice.
Whisk the cornstarch with cold water to make a slurry. Stir it into the liquid in the crockpot, cover, and cook on High for 10–15 minutes until the sauce thickens.
Combine: Return the chicken to the crockpot and add the broccoli. Toss to coat everything in the sauce.
Finish and serve: Taste and adjust seasoning—add a splash more soy sauce for salt, or a bit more honey/brown sugar for sweetness.
Serve over rice and sprinkle with sesame seeds and green onions.