Place the top sirloin steak chunks in a large bowl. Add the mirin, minced garlic, ginger paste, 1 teaspoon sesame oil, white pepper, and a generous pinch of Kosher salt. Toss all ingredients to fully combine, ensuring steak chunks are thoroughly coated. Set aside to marinate for at least 30 minutes.
In a large skillet or wok, heat 2 tablespoons unsalted butter and 1 tablespoon sesame oil over medium heat. When hot, add the carrots, zucchini, and mushrooms. Cook the vegetables, tossing often, until tender and golden brown, about 10-15 minutes. Season with garlic powder, salt, and pepper to taste. Transfer to a clean plate and set aside.
In the same pan, add the remaining 2 tablespoons butter and 1 tablespoon sesame oil over medium-high heat. When hot, add the marinated steak. Cook, tossing beef often, until nicely seared on all sides, about 3-4 minutes. Be careful not to overcook the steak into toughness.
Remove from heat and drizzle in the teriyaki sauce or Japanese BBQ sauce. Toss well to coat the steak chunks in sauce until they're glistening.
To assemble, evenly divide the warmed fried rice among shallow bowls. Top each bowl with the hibachi steak and sautéed vegetables. Drizzle with yum yum sauce and garnish with sliced green onions and black sesame seeds. Serve immediately while hot.