Marinate the steak. Place the sirloin chunks in a large bowl or resealable bag. Add the mirin, minced garlic, ginger paste, 1 teaspoon sesame oil, pepper, and salt. Toss until the steak is evenly coated. Marinate for at least 30 minutes.
Cook the vegetables. Heat 2 tablespoons butter and 1 tablespoon sesame oil in a large wok or skillet over medium heat. Add the carrots, zucchini, and mushrooms. Cook, tossing frequently, for 10–15 minutes, or until the vegetables are tender and lightly browned. Season with garlic powder, salt, and pepper. Transfer the vegetables to a clean plate.
Sear the steak. Add the remaining 2 tablespoons butter and 1 tablespoon sesame oil to the same pan. Increase the heat to medium-high. Once hot, add the marinated steak in a single layer as much as possible. Cook, tossing occasionally, for about 3–4 minutes, until browned and cooked to your preferred doneness. For the best Hibachi Steak Bowls, avoid overcrowding the pan so the beef sears rather than steams.
Add the sauce. Remove the pan from the heat and drizzle the teriyaki or Japanese BBQ sauce over the steak. Toss until every piece is glossy and coated.
Assemble the bowls. Divide the fried rice, seared steak, and sautéed vegetables among shallow bowls. Drizzle with Yum Yum sauce or serve the sauce on the side.