1. In a pot of salted boiling water, cook the rice for 20 minutes. Drain, return to the pot, and add the butter. Mix, cover, and set aside. Wash the vegetables, peel the carrots, and cut them, along with the zucchini, into small cubes. In a small bowl, whisk together the soy sauce, cornstarch, and 2 tablespoons of water.
2. In a pan with 2 teaspoons of olive oil, sauté the carrot and zucchini cubes over high heat for 10 minutes, stirring regularly. Add the bean sprouts and continue cooking for 5 minutes, still over high heat. Add the soy sauce/cornstarch/water mixture, gently mix, and stop cooking. Set aside in a separate dish.
3. In the same pan, pour the remaining oil. Cook the fried eggs, lightly salt and pepper them. Separate the 4 fried eggs. In 4 bowls, place a fried egg at the bottom (yolk side down), distribute the sautéed vegetables on top, then the cooked rice. Press lightly. Flip each bowl onto a plate: the yolk will run. Serve immediately.