Stir in stock and rice; bring to boil. Reduce heat, cover and simmer until rice is tender, about 20 minutes. Stir in bean sprouts and half of the green onions.
Meanwhile, in bowl, whisk together eggs, water and remaining salt and pepper. In 8-inch nonstick skillet, heat 1 tsp of the butter over medium-high heat. Pour in one-quarter of the egg mixture; cook, lifting edge to allow uncooked eggs to flow underneath, until almost set, about 3 minutes. Turn and cook until completely set, about 5 minutes. Repeat to make 4 omelettes.
Spoon one-quarter of the rice mixture onto 1 side of each omelette crepe; fold over. Sprinkle with remaining onions.