Start by steaming the rice. Bring 3 cups of water to a boil in a pot, stir in the 3 cups of rice, cover with a lid, and turn off the heat. Allow to stand for 10 minutes. Fluff with a fork.
On a griddle (or in a large skillet), put a drizzle of oil and cook the onion, carrots, zucchini, and mushrooms, stirring occasionally. Season with salt and pepper to taste. Cook for about 20 minutes, and when they’re softened, pour on Japanese BBQ sauce (about 1/3 cup or to taste), and stir well to combine. Keep warm over low heat.
While the veggies cook, start the fried rice. Place a drizzle of oil on the griddle over medium heat, and spread the rice into an even layer. Pour about 1/4 cup of Japanese BBQ sauce, the steamed mixed veggies, and the 2 eggs onto the rice, and stir well to combine. Spread back into an even layer and lower the heat to keep warm.
While the rice and veggies cook, start the meat. Place a drizzle of oil on the griddle over medium heat, sear the meat, season with salt and pepper to taste, and coat with about 1/4 cup (or to taste) of the Japanese BBQ sauce, and stir well to combine. The chicken will need the longest time, about 10-12 minutes or until cooked through, followed by the steak for 8-10 minutes, and then the shrimp for only about 5-6 minutes, until they’re just pink.
Remove everything from the griddle and layer into a bowl, with fried rice as the base. Drizzle with Yum Yum sauce to finish.