Thinly chop onion and carrot. Cut small pieces of chicken thigh into tiny pieces.
Heat a frying pan over high heat, add 1 tbsp of oil. Stir-fry onion until it turns translucent.
Add the carrot and continue to stir-fry. Add the chicken and cook until the meat changes color.
Add 1.5 cups of warm Japanese white rice, and keep on stir-frying.
Season with salt and black pepper, and stir-fry everything together.
Move the rice to one side of the pan to make a little space. Add just a bit of oil, then 3 tbsp of ketchup. Cook the ketchup briefly and mix it into the rice.
Place the rice on a plate and shape it like a small mountain.
Crack 3 eggs into a bowl. Add 1 tbsp of milk and mix well.
Heat a small frying pan over high heat, and add 2 tbsp of butter, melting them completely.
When the butter starts bubbling, pour in the eggs. Using chopsticks, stir-constantly. When the eggs are still very soft, turn off the heat.
Gently push the eggs to one side with a rubber spatula to make the omelet. You could do this process away from the heat by placing the pan on a cold wet towel, if you don't want to rush too much.
Carefully place the omelet on top of the rice.
Slice the center of the omelet lengthwise with a sharp knife, opening slowly. Then open over the rice.
Adding demi-glace sauce around the rice is an option. Also, you can make a ketchup decoration on top of the omelet. It's ready! We hope you enjoy your "TOKYO FLAVORS, NEW YORK STYLE" meal! Itadakimasu!