Prep the chicken and broccoli: Pat the chicken dry, then season with salt and pepper. Cut broccoli into bite-size florets so they cook quickly and evenly.
Whisk the sauce: In a small bowl, combine soy sauce, honey, rice vinegar, sesame oil, and broth. Stir in garlic and ginger.
Set aside.
Heat the pan: Place a large skillet over medium-high heat. Add oil and let it get hot—shimmering but not smoking.
Sear the chicken: Spread the chicken in a single layer. Cook 4–6 minutes, stirring once or twice, until browned and nearly cooked through.
Remove to a plate.
Cook the broccoli: Add broccoli to the same skillet with a splash of water (1–2 tablespoons). Cover for 2 minutes to steam, then uncover and stir until bright green and crisp-tender.
Bring it together: Return chicken to the skillet. Give the sauce a stir and pour it in.
Simmer 1–2 minutes, letting flavors meld.
Thicken the sauce: Stir the cornstarch slurry, then drizzle it in while stirring. Cook 30–60 seconds until the sauce turns glossy and coats the chicken and broccoli.
Taste and adjust: Add a pinch more salt, a squeeze of lime, or a dash of red pepper flakes if you want extra heat. It should taste balanced—sweet, savory, and garlicky.
Serve: Spoon over warm rice or noodles.
Garnish with green onions and sesame seeds.