"We found Japanese omurice when searching for a new Meatless Monday dish. I made it my 'Om' by adding more veggies. In Minnesota it is common to have ketchup with your eggs, but if that seems odd, just try it, the flavors go really well together."
Place potato and carrot in a microwave-safe bowl; heat in microwave until tender, 5 to 10 minutes. Cool until easily handled. Peel potato and dice.
Heat olive oil and 1 tablespoon butter in a skillet over medium heat; cook and stir onion and red bell pepper until tender, 5 to 10 minutes. Add potato, carrots, rice, and peas; cook and stir until heated through, about 2 minutes. Stir ketchup into mixture.
Whisk eggs, egg whites, milk, salt, and pepper together in a bowl.
Heat a non-stick skillet over medium heat; melt 1 1/2 teaspoons butter. Pour 1/2 of the egg mixture into skillet and cook until set, pulling sides up with a spatula to let uncooked egg run under to cook, about 5 minutes. Spoon 1/2 of the rice mixture onto 1 side of cooked egg and fold egg over; continue to fold egg over until seam is on the bottom. Slide omelet onto a serving plate. Repeat with remaining butter, egg mixture, and rice mixture.
Squeeze a curvy line of ketchup down the center of each omelet before serving.
You can add or subtract veggies to your family's taste. You can also add cooked chicken. You can get the same effect by plating the rice and then topping with the cooked egg if filling and rolling the omelette is too difficult or time consuming.