Chop the onion, carrot, and ham into small pieces.
Heat oil in a pan and sauté the vegetables and ham.
Add rice, then season with salt, pepper, and ketchup, and stir-fry.
Beat the eggs and cook them into a thin omelet in a separate pan.
Place the fried rice onto the omelet and fold the omelet over the rice.
Transfer to a plate and drizzle ketchup on top.