Prepare the Ketchup Rice

Place rice in a large bowl, and add water to cover to a depth of 1 inch; let soak for 30 minutes. Drain rice; place rice in a rice cooker’s inner pot or a medium pot with a tight-fitting lid. Add 1 1/2 cups water, ketchup, Worcestershire sauce, and salt; stir using chopsticks or a fork until combined.

Place bacon in a cold medium skillet; cook over medium, stirring occasionally, until slightly crispy at edges, about 8 minutes. Add onion, and cook, stirring occasionally, until softened, about 3 minutes. Place bacon, onion, and bay leaf on top of rice. Do not stir. If using an electric rice cooker, close lid, and choose setting for regular white rice. If using a medium pot, cover pot, and bring to a boil over medium-high. Reduce heat to medium-low, and simmer, undisturbed, for 15 minutes. Turn off heat, and let rice stand for 10 minutes. Add butter, and stir using rice paddle or spatula until butter is melted and evenly combined. Discard bay leaf.

Prepare the Omelets

Crack 2 eggs into a small bowl. Add 1 tablespoon of the water, and sprinkle with 1/8 teaspoon of the salt and a pinch of the pepper. Stir well using chopsticks or a fork until fully combined. Melt 1 tablespoon of the butter in a nonstick 10-inch skillet over medium. Add egg mixture; swirl skillet over heat, stirring constantly using chopsticks, until small curds form and eggs are custardy, about 30 seconds. Let cook, undisturbed, until nearly set, 30 seconds to 1 minute. Add 3/4 cup Ketchup Rice to center of omelet, and fold both sides over, shaping into a football. Slide onto a plate, seam side down. Repeat process with remaining eggs, water, salt, pepper, butter, and 2 1/4 cups Ketchup Rice. Reserve remaining 1 cup Ketchup Rice for another use. Top each omelet with about 1 tablespoon ketchup, and serve.