Toss the sliced beef with 1 tablespoon cornstarch and 1 tablespoon soy sauce until every piece is lightly coated. Let it sit while you prep everything else — this is the velveting step that keeps it tender.
Whisk all the sauce ingredients together in a bowl, making sure the cornstarch fully dissolves. Set it next to the stove.
Heat 1 tablespoon of oil in a large skillet or wok over high heat until shimmering. Add the broccoli and 2 tablespoons of water, cover, and steam 3 minutes until bright green and crisp-tender. Transfer to a plate.
Add another tablespoon of oil to the empty pan. Sear half the beef in a single layer, undisturbed, for 1 minute, then toss for 30 seconds more. Remove and repeat with the remaining oil and beef.
Return all the beef and the broccoli to the pan. Give the sauce a quick whisk and pour it in.
Toss constantly for 1 to 2 minutes as the sauce bubbles and thickens into a glossy coating. Serve immediately over rice.