Prepare your ingredients: slice the chicken into evenly sized pieces and wash the broccoli florets. Have the garlic and ginger minced and ready; this keeps the steam cooking smooth and quick.
Set up a steamer: fill a pot with about 1 inch of water and bring to a gentle boil. Place a steamer basket or a wide, heatproof plate above the water level and cover.
Season the chicken lightly with a pinch of salt and pepper. In a small bowl, whisk together soy sauce, rice vinegar, sesame oil (if using), garlic, ginger, and red pepper flakes. If you plan to create a glaze, mix cornstarch with water in a separate tiny bowl.
Layer the chicken into the steamer basket, then lay the broccoli on top. The goal is a single layer so the steam can circulate. If you need to, do this in two batches.
Place the basket over the simmering water, cover, and steam for about 6–8 minutes, or until the chicken reaches 165°F (74°C) and the broccoli is bright green yet crisp-tender.
Carefully remove the steamer basket and transfer to a serving dish. If you’re making a glaze, pour the soy-ginger mixture over the chicken and broccoli, then gently toss to coat. If using a cornstarch slurry, simmer the sauce in a small pan for 1–2 minutes until slightly thickened, then drizzle over the dish.
Finish with optional garnish: scatter scallions and sesame seeds for color and aroma.