Croquettes have almost universal appeal, because who doesn’t like starchy fried things? The Japanese version of croquettes, called korokke, is very adaptable, which means its great for using up small bits of meat, seafood and vegetables in the fridge. If you like, make vegetarian croquettes by omitting the beef and adding more vegetables (blanched peas and/or corn kernels are good). If you're feeding children (or others with sensitive palates) then decrease the amount of curry powder.
The fried croquettes taste good hot, warm and at room temperature. They can be reheated in the oven.
Panko are Japanese bread crumbs. Shichimi togarashi is seven spice mixture; if you don't have it, subsitute a little chilli powder mixed with sesame seeds.
Scrub the potatoes then put them unpeeled in a saucepan and add cool water to cover by about 2.5cm (1in). Place the pan over a high flame and bring to the boil. Lower the heat, partially cover the pan with the lid and simmer the potatoes until just tender but not mushy. Drain the potatoes in a colander. When the potatoes are still warm but cool enough to handle, strip off and discard the skin. Mash the potatoes until smooth, then set them aside to cool.
Finely dice the onion and carrot. Heat about 15ml (1tbsp) of oil in a skillet and when it’s hot, add the onion and carrot and cook over a low flame until the carrot is tender.
Turn the flame to high, add the beef, then mix in the curry powder, sugar and ½tsp of salt. Cook, stirring often, just until the beef loses its pink colour. Cool to room temperature. Add the beef and vegetable mixture to the potatoes, sprinkle in 1 tsp of salt and some black pepper and mix well. Refrigerate for at least one hour, or until well chilled.
Taste the croquette mixture and mix in more curry powder and/or, salt if needed. Form the mixture into 16 to 18 evenly sized shapes (I like ovoids but you can make them into cylinders or thick discs).
Put some flour into a shallow bowl, the eggs (whisked) into a second bowl, and panko into a third. Lightly coat the croquettes with flour, then dip them in the egg and finally into the panko, pressing gently so the breadcrumbs adhere.
Pour cooking oil to the depth of about 4cm into a pan and heat over a medium flame to 170°C (340°F). Fry the croquettes several at a time in the oil, turning them over as necessary so they brown evenly. Adjust the flame to maintain the oil temperature as close as possible to 170°C/340°F. Fry the croquettes in batches; do not crowd the pan. When the croquettes are medium brown, drain them on paper towels.
Serve the croquettes with Kewpie mayonnaise dusted lightly with shichimi togarashi.