Prep the eggplant - Remove the stem end of the eggplant and slice the eggplant into chunks.
Make the Teriyaki marinade and marinate the eggplant - In a large bowl, add the tamari, water, brown sugar, mirin, rice vinegar, and oil. Peel the garlic. Using a hand grater or a rasp, grate the garlic and the ginger into the bowl with the vinegar mixture. Whisk to combine. Add the eggplant and stir to coat. Marinate for 2 hours, stirring occasionally. After two hours, scoop out the eggplant with a slotted spoon, and reserve the marinade.
Velvet the steak - Carefully trim the steak, then cut it into 2 inch by 1/4 inch slices. Coat the beef slices with 1 T tamari, 1 t cornstarch and 1/4 t baking soda. Stir until the cornstarch is no longer visible. Pour in 1 t sesame oil and give it a good stir, then let rest for 10-15 minutes.
Chop the green pepper and mince the scallions - while the steak is resting, chop the green pepper into wide strips about 2 inches long, and mince the scallions.
Brown the steak - Preheat your wok or skillet, then add some oil, and heat until shimmering. Add the steak in batches, to avoid steaming it. Leave it alone until it caramelizes and then stir it, and let it continue to brown. When just cooked on the outside, remove the beef from the pan and set it aside.
Cook the veg - Add the eggplant to the pan, and cook it for a few minutes, stirring constantly, then cover the pan and steam it until the eggplant softens begins to collapse. You want it to be cooked thoroughly. Add the green peppers and stir-fry until just crisp-tender.