In a shallow bowl, whisk together 3 tablespoons of the soy sauce with black pepper. Add the beef and turn it over, making sure to coat all sides of the steak. Cover and refrigerate the meat for 30 to 60 minutes. While the beef is marinating, whisk together the rest of the soy sauce with cornstarch and beef broth in a small mixing bowl; set it aside for later.

Once the beef has sufficiently marinated, drain the marinade and discard it. Heat canola oil in a large nonstick skillet or a wok for one minute, or until the oil is hot enough to sizzle. Stir-fry the garlic and ginger root for one minute, then add the beef to the skillet and stir-fry it for four to six minutes, or until the beef is no longer pink when you cut it. Remove the beef from the skillet and transfer it to a plate or bowl, then keep it warm.

Add the remaining oil to that same skillet or wok. Stir-fry the bell peppers for one minute, then add in the mushrooms and toss for another two minutes, or until the peppers are crisp-tender. Stir in the small bowl of sauce, then wait for the liquid to come to a boil. At this point the sauce will start to thicken, so cook and stir for another two minutes, until your vegetables are coated with thick sauce. Return the cooked slices of beef to the pan, as well as your slices of tomatoes and green onions. Stir-fry for another two minutes, or until everything is heated through. If desired, serve your Chinese pepper steak on a bed of rice and sprinkle it with sesame seeds and sliced scallions.