Add sliced steak, 2 Tablespoons gluten-free Tamari, and 1 Tablespoon gluten-free flour or cornstarch to a large Ziplock bag then seal and squish to evenly coat. Place the bag into the refrigerator to marinate while you prepare the rest of the dish.

Add remaining 1/2 cup gluten-free Tamari, remaining 1-1/2 Tablespoons gluten-free flour or cornstarch, chicken broth, brown sugar, 2 Tablespoons water, rice vinegar, sesame oil, garlic, ground ginger/ginger paste, and red chili pepper flakes to a bowl then whisk to combine and set aside.

Heat a large wok or nonstick skillet over high heat then add remaining 1/4 cup water. Once simmering, add broccoli then stir fry until crisp tender, 2-3 minutes. Remove to a plate then set aside.

Heat 1 Tablespoon oil in wok then, once very hot, add 1/2 the marinated beef in a single layer. Let sit undisturbed until browned on the bottom, 30 seconds, then stir fry until just barely cooked through (some pink still showing is ok.) Remove to plate with broccoli. Heat remaining Tablespoon oil then stir fry remaining beef and add to plate.

Add sauce to wok then simmer until slightly thickened, 2-3 minutes. Add cooked broccoli and beef back into the wok then simmer until everything is heated through, 1 minute. Serve over cooked rice.