Pat the thinly sliced beef strips dry with a paper towel and add them to a medium bowl. Sprinkle baking soda on the beef, and toss and massage the beef to thoroughly coat with the baking soda. Cover the bowl with plastic wrap and refrigerate for about 20 minutes. Remove the bowl from the refrigerator, and rinse the beef well under cold water. Pat the beef strips dry with a paper towel to remove the excess moisture.
While beef is marinating, in a medium bowl whisk together all sauce ingredients until thoroughly combined. Taste and add more red pepper flakes, siracha, or brown sugar to your liking. Set to the side. *The traditional beef and broccoli brown sauce is mild in flavor.
Preheat griddle on low until it reaches about 375 - 400°F.
Add about 2 tablespoons of cooking oil (I prefer avocado oil) to the heated griddle surface and spread it around with your spatula.
Add the beef strips to the griddle in a thin even layer, and allow the beef to cook untouched on the first side for about 60-90 seconds. Season with fresh cracked black pepper, sauté together for about 30-60 seconds, and move the beef to the cool side of the griddle so that it does not overcook. *If you are worried about the beef overcooking, you can remove it from the griddle until it's time to mix it with the broccoli.
Immediately after adding the beef to the griddle, begin cooking the broccoli on the griddle as well. After you move the beef to the side of the griddle, move the broccoli to the hotter zone on the griddle, add black pepper, and sauté for about 2-3 minutes.
Slowly pour about half of the prepared sauce over the broccoli and sauté together. The heat from the sauce will help to cook the broccoli more quickly.
Mix the beef in with the broccoli and add the remaining sauce. Saute everything together for an additional 1-2 minutes so the sauce has a chance to thicken. The sauce will also continue to thicken as the dish cools.
Remove the beef and broccoli from the griddle, garnish with sesame seeds or sliced green onions, and serve.