Place the sirloin pieces in a large bowl. Add the rice vinegar, minced garlic, ginger paste, 1 teaspoon sesame oil, white or black pepper, and salt. Toss thoroughly so every piece of steak is coated.
Cover and refrigerate the steak for at least 30 minutes. Remove it from the refrigerator shortly before cooking.
Heat 2 tablespoons butter and 1 tablespoon sesame oil in a large skillet or wok over medium heat.
Add the carrots, zucchini, and mushrooms. Cook for 10–15 minutes, tossing regularly, until the vegetables are tender and develop golden-brown edges.
Season the vegetables with garlic powder, salt, and pepper. Transfer them to a clean plate and set aside.
If necessary, carefully wipe the skillet clean. Return it to the stove and increase the heat to medium-high.
Add the remaining 2 tablespoons butter and 1 tablespoon sesame oil.
Once the skillet is hot, add the marinated steak. Arrange the pieces with enough room around them to encourage browning. Cook for approximately 3–4 minutes, tossing occasionally, until nicely seared and cooked to your preferred doneness. Work in batches if your skillet is not large enough.
Remove the skillet from the heat. Drizzle 1–2 tablespoons teriyaki or Japanese-style BBQ sauce over the steak and toss until the pieces are lightly coated and glossy.
Divide warm fried rice among shallow serving bowls. Arrange the steak and sautéed vegetables over the rice.
Finish the Hibachi Steak Bowls with Yum Yum sauce or serve the sauce on the side.