Make the sauce: In a saucepan, melt unsalted butter over low heat. Stir in all-purpose flour and cook until brown, about 4-5 minutes. Gradually add water, stirring until combined. Add sugar, mirin, ketchup, Worcestershire sauce, chicken bouillon powder, and black pepper. Bring to a boil, then simmer for 3 minutes.
Prepare vegetables: Finely chop garlic, carrot, and onion.
Make fried rice sauce: In a small container, mix ketchup, mirin, and Worcestershire sauce.
Cook fried rice: In a large wok or pan, heat oil over medium-high heat. Add ground beef and cook until brown. Add garlic, carrot, onion, and fried rice sauce. Stir for 2-3 minutes until onion is translucent. Increase heat to high, add rice, and stir-fry for 3-4 minutes. Season with salt and pepper.
Prepare omelette: Beat eggs with a pinch of salt. In a medium pan, heat oil over medium heat. Add half of the beaten eggs and cook until the bottom is set but the top is slightly runny.
Assemble Omurice: Place fried rice in a bowl, press down, then invert onto a plate. Slide the omelette over the rice. Pour the prepared sauce over the omelette. Garnish with heavy cream and parsley if desired.