Crack the whole eggs into a small mixing bowl. Add dashi powder or salt then whisk until fully combined. Set aside for later
Heat neutral oil in a pan over medium heat. Toss in the onions, carrots, and garlic and stir fry until tender and fragrant, about 1 to 2 minutes. Add the cold day-old rice and break it apart using a spatula or wooden spoon.
Add soy sauce, ketchup, and Worcestershire sauce and mix until thoroughly combined. Toss in chopped scallions and give it a final mix.
Divide the fried rice into two serving portions. To make a dome, fill the fried rice into a rice bowl and pack it down. Flip the rice bowl onto a plate. Remove the bowl then set the plate aside.
In a small pan (4 to 6 inches), heat 2 tablespoons neutral oil over medium-low heat. Once the oil is hot, pour half the egg mixture from earlier. Top it with an egg yolk then break it apart using a chopstick. Immediately drag a pair of chopsticks to the center of the pan, making sure they are about 1 to 2 inches apart. Gently and carefully rotate the chopsticks to create a swirl. Continue swirling until the eggs are almost set. The eggs will continue cooking from the residual heat.
Transfer the tornado egg omelette over the fried rice. Repeat for the second serving.
Garnish with dried parsley flakes and chili flakes.