Heat butter in a skillet over medium heat. Sauté chicken, onion, carrot, and bell pepper. Season with salt and pepper. Cook until the chicken turns white and the vegetables soften. Add rice, barbecue sauce, chicken bouillon powder, garlic powder, and black pepper. Stir until evenly coated and heated through.

Pack the rice tightly into a small bowl. Press firmly with a spoon. Place a plate over the bowl and flip to unmold onto the serving plate.

In a bowl, mix eggs and mayonnaise thoroughly until completely smooth.

Heat oil in a 7–8 inch skillet over medium heat. Pour in the egg mixture. Using chopsticks or a spatula, gently stir in circular motions until the eggs begin to set and the bottom of the pan becomes slightly visible.

When mostly set but still soft on top, cover with a lid, turn off the heat, and let sit for 1 minute. Carefully slide the omelette over the rice mound.

For the sauce, sauté onion and shiitake in butter until softened. Add flour and cook until no dry flour remains. Stir in water, barbecue sauce, and soy sauce, whisking constantly until thickened. Add milk and bring to a gentle simmer until smooth.

Pour the sauce over the omurice and garnish with parsley.