Omurice (Omelette Rice)

Name: Omurice (Omelette Rice)
Prep time: 10 min
Cook time: 35 min
Total time: 45 min
Cuisine: Asian, Japanese
Ingredients: 1.5 Tbsp cooking oil ((I used rice bran oil)); 1 Tbsp plain flour; 5 Tbsp ketchup; 1 Tbsp soy sauce (, regular (kikkoman)); 1 Tbsp Tonkatsu sauce (or regular soy sauce); 1 Tbsp honey (or brown sugar); 3/4 cups water; 1/4 cups milk; Some cooking oil; 1/2 carrot ( (60g / 2 ounces), finely chopped); 1/2 onion ((80g / 2.8 ounces), finely chopped); 1/3 green bell peppers ((45g / 1.6 ounces), finely chopped); 80 g smoked ham (2.8 ounces, (e.g Strasburg meat), finely diced or minced beef, pork or chicken); 2 cups cooked rice ((short or medium grain), cooled); 1 Tbsp ketchup ((or more if not serving with the demi-glace sauce above)); 1 Tbsp Worcestershire sauce; 1 Tbsp soy sauce (, regular (kikkoman)); 1 Tbsp rice wine ((mirin)); Some cooking oil; 6 eggs ((3 eggs per serving)); A pinch salt