Preheat the oven to 350 degrees F.
Cook the rice in the water according to package directions. For best results, spread the cooked rice in a shallow metal pan and stick it in the freezer to cool quickly. Do not let it freeze, though. If you don’t have time to chill the rice, just spread it out so it cools completely.
While the rice is cooking and cooling, spread the sesame seeds in a shallow baking pan. Bake until golden brown, 10 to 15 minutes, shaking pan occasionally for even color. Remove from the oven.
Melt the butter in a large skillet. Add the onions, carrots, and scallions. Cook, stirring from time to time, until the onions are translucent. Remove from the heat and set aside. Heat another large skillet or a wok if you have one. Add a splash of oil and swirl it around. Pour the eggs into the hot skillet. Cook as you would scrambled eggs. When the eggs are barely done, add the vegetables, rice, 2 tablespoons of the garlic butter (you can add more if desired) and sesame seeds and sprinkle with the soy sauce. Stir-fry until everything is mixed and hot. Season with salt and pepper to taste.
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Recipe Tips
For authentic Benihana flavor, don't skimp on the garlic butter—it's truly the secret ingredient. Using day-old cold rice is crucial as freshly cooked rice will become mushy. If you're short on time, cook the rice a few hours ahead, spread it on a baking sheet, and refrigerate until thoroughly chilled. For extra authenticity, try using safflower oil, which is what Benihana chefs use for its neutral flavor and high smoke point.