Donburi is a Japanese dish in which either meat, fish, or eggs are served over rice.
Place rice and 2 cups water in a medium saucepan. Set saucepan over high heat; bring water to a boil. Cover saucepan, and reduce heat to a bare simmer. Cook rice until water has been absorbed, about 20 minutes. Remove saucepan from heat, and set rice aside, covered, until ready to serve.
In a medium bowl, lightly whisk together whole eggs, egg whites, and black pepper. Set the egg mixture aside.
Place a medium nonstick skillet over medium-high heat. When hot, spray skillet with olive-oil cooking spray. Add mushrooms; saute until browned, 2 to 3 minutes.
Add the snow peas, carrot, and all scallions to the skillet. Cook until snow peas turn bright green in color, about 1 minute.
Add the vegetable stock, ginger, and soy sauce to the skillet. Cook until the liquid has been reduced by half, about 6 minutes. Gently pour in the reserved egg mixture without stirring. Cover the skillet, and cook until eggs have just set, 4 to 5 minutes.
Divide the rice among 4 soup plates or soup bowls. Divide omelet into 4 servings; spoon omelet and any remaining broth over the rice. Garnish with radish sprouts.