Place the sirloin or round steak in the freezer for about 15 minutes to firm it up. Slice the beef against the grain into strips about 1 inch (2.5 cm) wide and 3 inches (7.5 cm) long.
In a small bowl, combine the hot beef broth, soy sauce, Worcestershire sauce, brown sugar, ground ginger, minced garlic, and black pepper. Whisk until the brown sugar dissolves completely. Add red pepper flakes now if you want a spicy version.
Add the sliced beef to the bottom of the slow cooker. Pour the sauce evenly over the beef and stir gently to coat. If you like soft peppers and onions, add them now; for firmer vegetables, hold them back until the last hour of cooking.
Cover and cook on LOW for 6 hours or HIGH for 3 hours. The beef is ready when it's fork-tender and the vegetables have softened. Avoid lifting the lid during cooking.
If you reserved the vegetables for firmer texture, stir in the bell peppers and onion during the final hour of cooking. Push them down into the sauce so they steam and soften evenly.
In a small bowl, whisk the cornstarch into the cold water until smooth with no lumps. Stir the slurry into the slow cooker. Switch to HIGH, cover, and cook for another 20 to 30 minutes until the sauce turns thick and glossy.
Give everything a final stir to coat the beef and vegetables in the thickened sauce. Spoon over hot cooked white rice and serve right away.