Omurice with demi-glace sauce

Name: Omurice with demi-glace sauce
Cook time: 1 h
Total time: 1 h
Cuisine: Japanese
Ingredients: 1 Tablespoon ketchup; 1 1/2 Tablespoon Worcestershire sauce; 1/2 Tablespoon Tonkatsu sauce (HERE to buy); 1 teaspoon sugar; 1 teaspoon soy sauce (HERE to buy); 5 g unsalted butter; 10 g unsalted butter; 60 g vegetable mix (I used THIS. ); 175 g cooked Japanese rice (HERE is how to make rice); 1/4 teaspoon salt; 1/4 teaspoon freshly ground black pepper; 2 large egg(s); 1 1/2 Tablespoon milk; 5 g butter