Make the Sauce: In a bowl, combine the hot water, soy sauce, brown sugar, sesame oil, cornstarch, garlic, ginger, and black pepper. Whisk together until the sugar fully dissolves. Set aside.

Cook the Broccoli: Heat 1 tablespoon of oil in a large skillet over medium heat. Add the broccoli and cook it partially covered, stirring occasionally, for 4 to 5 minutes, or until it becomes bright green and tender-crisp. Transfer the broccoli to a plate.

Cook the Beef: Increase the heat to high and add the remaining tablespoon of oil to the skillet. Add the beef strips in a single layer and cook for about 2 minutes on each side, or until they are just browned.

Combine Everything: Lower the heat to medium and pour the sauce into the skillet with the beef. Stir well and simmer for 3 to 4 minutes, allowing the sauce to thicken slightly. Return the broccoli to the skillet and mix everything until evenly coated. If the sauce becomes too thick, stir in 1 to 2 tablespoons of water to reach your desired consistency.

Serve: Serve the stir-fry hot over a bed of steamed rice, and sprinkle with sesame seeds for garnish.