1. Begin by peeling the Russet or Idaho potatoes and cutting them into chunks. Place them in a pot of cold salted water, bring to a boil, and cook for about 10-15 minutes or until tender. Drain thoroughly and let the potatoes sit momentarily to remove excess moisture.
2. Mash the drained potatoes with milk and butter until smooth. Add salt, pepper, and optionally dashi powder for extra flavor. Set aside.
3. In a separate pan, sauté chopped onion, grated carrot, minced garlic, and ground beef (or your protein of choice) until the meat is browned and the vegetables softened. Add soy sauce and sugar, stirring to incorporate the flavors.
4. Combine the mashed potatoes and the meat-vegetable mixture in a bowl. Mix thoroughly to ensure all ingredients are evenly distributed.
5. Let the mixture cool to room temperature, then chill it in the refrigerator for approximately 20 minutes to firm up.
6. Once the mixture is firm, divide it into equal portions and shape each piece into thick oval patties about 1 inch thick, ensuring there are no cracks.
7. Prepare a coating station with three shallow bowls: one with flour, one with beaten eggs, and one with panko breadcrumbs. Dredge each patty in flour, dip in the beaten egg, and coat thoroughly with panko.
8. Heat oil in a deep frying pan to approximately 350°F (180°C). Test the oil with a small piece of bread; if it lightly browns, the oil is ready. Fry the patties in batches, cooking about 2-3 minutes per side until golden brown. Avoid overcrowding the pan.
9. For a healthier option, preheat an air fryer to 400°F (200°C). Spray or lightly brush the korokke with oil, place them in the fryer basket in a single layer, and cook for 7 minutes, flipping halfway through.
10. Once fried, transfer the croquettes to a plate lined with paper towels to drain any excess oil.
11. Serve the crispy korokke hot, accompanied by shredded lettuce, tonkatsu sauce, or your preferred sides, such as a fresh salad or steamed rice.