Prepare the Teriyaki Sauce by combining soy sauce, brown sugar, ginger, and garlic in a saucepan over medium heat. Stir until the sugar dissolves and the mixture thickens slightly, taking about 5-7 minutes. Set aside to cool, reserving ¾ cup for marinating the flank steak.

In a zip-top bag, combine the sliced flank steak with the reserved ¾ cup of teriyaki sauce. Seal the bag and gently massage the steak for an even coating. Marinate in the refrigerator for at least 30 minutes or overnight.

Preheat your oven to 350°F (175°C). In a large skillet, heat a tablespoon of oil over medium heat. Add 4 cups of day-old cooked rice, breaking up any clumps. Stir-fry for about 3 minutes until heated through.

Push the rice to one side of the skillet and add a whisked egg to the empty space. Scramble for about 2-3 minutes until fully cooked, then combine with the rice.

In a large baking dish, combine the fried rice, sliced marinated flank steak, and mixed vegetables. Toss together to distribute flavors and colors.

Pour the remaining teriyaki sauce over the mixture, ensuring everything is well-coated. If desired, bake for about 10-15 minutes for a crispy top.

Allow to cool for a few minutes before garnishing with chopped green onions and toasted sesame seeds. Serve warm.