Cut chicken into bite-sized pieces. Trim the root of enoki mushrooms and cut into thirds.

Place chicken and sake in a microwave-safe container, cover loosely with plastic wrap, and microwave at 600W for 2 minutes. Add butter and ketchup, mix well, then stir in the rice until evenly combined.

In another microwave-safe container, combine enoki mushrooms, ketchup, and Worcestershire sauce. Cover loosely with plastic wrap and microwave at 600W for 2 minutes to make the mushroom sauce.

In a frying pan, mix eggs, pizza cheese, milk, and cornstarch. Cook over low heat, stirring constantly, then increase to medium heat and cook for 1–2 minutes until the mixture thickens.