In a 2- to 3-cup microwave-safe bowl, mix rice and 1/2 cup water. Cover with plastic wrap and cook in a microwave oven on full power (100%) until water is absorbed, 4 to 5 minutes. Let stand.
Meanwhile, beat egg, egg whites, and 1 tablespoon water.
Add 1/8 teaspoon salt to eggs; blend.
In a 6- to 8-inch nonstick frying pan, stir cabbage and onion over high heat until onion begins to brown, about 3 minutes. Sprinkle with pepper to taste.
Reduce heat to medium. Pour egg mixture over cooked vegetables. As eggs set, use a wide spatula to lift cooked portion and let liquid flow underneath.
When golden on bottom and still moist on top, in about 2 minutes, loosen eggs from pan with spatula, then slide spatula under omelet on one side and flip about 1/3 of it over the center. Tilt pan to slide unfolded edge of omelet onto a plate, then tip pan to roll remainder of omelet onto that edge.
Sprinkle with slivered nori. Add salt and pepper to taste. Serve with hot cooked rice.
Notes: You can use 1/2 cup purchased egg substitute for the egg and skip step Nori is dried seaweed; furikake is a seasoning blend of dried fish flakes, sesame seed, and nori. Both are sold in Japanese food stores and well-stocked supermarkets.