Prep the chicken and broccoli. Pat the chicken dry and cut into 1-inch pieces. Season lightly with salt and pepper.
Cut broccoli into bite-size florets. If using fresh broccoli, rinse and shake dry.
Whisk the sauce. In a bowl, stir together soy sauce, honey, rice vinegar, mirin (if using), water or broth, sesame oil, garlic, ginger, and a pinch of red pepper flakes. In a small cup, mix cornstarch with equal water to make a slurry.
Set both aside.
Blanch or steam the broccoli (optional but recommended). For bright, crisp-tender broccoli, steam or blanch for 1–2 minutes until just tender, then drain. This keeps the stir-fry quick and prevents overcooking.
Sear the chicken. Heat 1 tablespoon oil in a large skillet over medium-high. Add half the chicken in an even layer.
Don’t move it for 2 minutes to get color, then stir and cook until mostly cooked through, 4–5 minutes total. Transfer to a plate. Repeat with remaining oil and chicken.
Bring it together. Return all chicken to the pan.
Add the broccoli. Give the sauce a quick whisk and pour it into the skillet. Bring to a simmer over medium heat.
Thicken the sauce. Once bubbling, stir in the cornstarch slurry.
Cook 1–2 minutes, stirring, until the sauce turns glossy and thick enough to coat a spoon. If it gets too thick, splash in a tablespoon of water.
Taste and adjust. Add more honey for sweetness, soy sauce for salt, or vinegar for brightness. A few drops of sesame oil at the end deepen the flavor.
Serve. Spoon over hot rice or toss with noodles.
Top with sliced green onions and sesame seeds. Add lime wedges if you like a citrus pop.