Heat the oven. Set to 425°F (220°C). Line a large sheet pan with parchment for easy cleanup.
Mix the marinade. In a bowl, whisk soy sauce, honey, rice vinegar, 1 tablespoon sesame oil, black pepper, and cornstarch if using.
Prep the chicken. Pat dry and cut large thighs into two pieces for even cooking.
Toss with half the marinade. Let sit 10–15 minutes while you prep broccoli.
Season the broccoli. On the sheet pan, toss florets with neutral oil, a pinch of salt, and sesame seeds. Spread to one side in a single layer.
Add the chicken. Place chicken on the other side of the pan.
Drizzle any remaining marinade from the bowl over the chicken only.
Roast. Bake 15 minutes. Stir broccoli, flip chicken, and brush with the remaining marinade. Roast another 8–12 minutes, until chicken reaches 165°F and broccoli is browned at the edges.
Make the scallion-ginger sauce. While it roasts, combine scallions, ginger, garlic, neutral oil, sesame oil, rice vinegar, soy sauce, sugar, and a pinch of salt.
Adjust to taste with more vinegar or soy. Add red pepper flakes if you like heat.
Finish and serve. Spoon the sauce over hot chicken and broccoli. Squeeze lime over the top if using.
Sprinkle extra sesame seeds. Serve with steamed rice or noodles.