Bring a large saucepan of water to the boil. Boil the potatoes until they are soft, about 15 minutes. Drain, mash and add the seasoning ingredients - salt, chicken stock granules and white pepper. Stir to mix and set aside to cool.
Meanwhile, mix together the tomato ketchup and Worcestershire sauce to make the dipping sauce. Set aside.
Heat a large frying pan with 1 tablespoon oil over high heat. Stir-fry the carrots and onions until soft, about 3-4 minutes. Pour into the mashed potatoes and mix.
Take a handful of the cool potato mix and shape it into a croquette shape. Dredge in cornflour, then dip into the egg, then breadcrumbs. Repeat until all of the potato is used up. Set on a dish and chill for 15 minutes.
Heat the oil in a large frying pan or deep-fat fryer. Fry the potato croquettes until lightly brown, about 3-4 minutes. Drain and set aside.
Reheat the oil over high heat and return the potato croquettes to the oil. Fry until golden brown, about 2-3 minutes. Drain and serve with the sauce.
Japanese breadcrumbs (panko) can be purchased in Chinese/Oriental speciality stores or online.