Heat olive oil in a large pot over medium heat. Add diced onions and sauté until translucent, about 3-4 minutes.
Add carrots and potatoes to the pot. Cook for 5-6 minutes, stirring occasionally.
Pour in dashi or chicken stock and bring to a boil. Reduce heat and simmer for 15-20 minutes until vegetables are tender.
Stir in ketchup and soy sauce, then add curry roux cubes. Stir until completely dissolved.
Mix cornstarch with water to create a slurry. Add to the curry and stir until thickened. Keep warm.
Beat 2 eggs with a pinch of salt and a dash of water for each omelet.
Heat butter in a non-stick pan over medium-low heat. Pour in beaten eggs for one serving.
When eggs are almost set but still slightly wet on top, place one serving of steamed rice in the center.
Carefully fold the omelet over the rice, sealing the edges. Slide onto a plate seam-side down.
Repeat with remaining eggs and rice for the second serving.
Ladle curry sauce over each omurice and serve immediately.