Start by preparing and marinating the meat. Place the beef slices in a bowl and mix them thoroughly with the tamari, grated fresh ginger, and minced garlic. Let this mixture sit briefly so the flavors can penetrate the meat.
Next, place a wok or large skillet on the heat and warm the sesame oil over high heat. As soon as the oil is hot, add the marinated beef slices. Stir-fry the meat for about two minutes until it's browned on all sides. Remove the beef from the pan and set it aside on a plate.
Use the same hot pan with the remaining cooking oil to prepare the vegetables. Add the red bell pepper slices and snap peas to the wok. Keep stirring continuously and stir-fry the vegetables for four to five minutes, until they are tender-crisp but still retain their crunch.
Finally, return the reserved beef slices, along with any meat juices left on the plate, back to the vegetables in the pan. Toss everything together well so the meat warms through and the flavors combine. Dish the meal directly from the pan onto plates and serve hot.