Place broccoli florets in a small bowl, fill with a few teaspoons of water and steam in microwave for 2 minutes.
Combine the sauce ingredients and divide it into half. Marinate the shrimp with one half of the sauce for 5-10 minutes (or up to 24 hours).
Heat a heavy-duty skillet to high heat. Add 1 tablespoon oil to pan then add the marinated shrimp. Sear them on both sides in batches of 2 until browned, about 1 minute per side. Add the broccoli to the pan, drizzle with remaining sauce, and mix well to combine.