In a small mixing bowl, whisk together the soy sauce, brown sugar, minced garlic, ginger, and black pepper until the sugar is dissolved.
In a separate small container, mix the cornstarch and cold water to create a smooth slurry.
Heat the vegetable oil in a large wok or skillet over high heat until shimmering.
Add the sliced beef in a single layer and sear without moving for 2 minutes, then flip and cook for an additional minute until browned; remove beef from the pan and set aside.
Add the broccoli florets to the same pan with 2 tablespoons of water, cover with a lid, and steam for 2 minutes until bright green and tender-crisp.
Return the beef to the pan and pour the soy sauce mixture over the ingredients.
Stir in the cornstarch slurry and cook for 1 to 2 minutes, tossing constantly, until the sauce has thickened and glossily coats the beef and broccoli.
Remove from heat and serve immediately over rice or noodles.