Peel and quarter the medium potatoes. Bring a large pot of water to a boil over medium-high heat. Add the potatoes and boil for about 15 minutes until fork-tender. Drain thoroughly and transfer to a large mixing bowl.
Heat 1 tablespoon (15 ml) vegetable oil in a pan over medium heat. Sauté the onions until softened and translucent, making sure any excess liquid has fully evaporated. Add them to the potatoes along with the salt, garlic powder, black pepper, and curry powder.
Gently mash the potatoes and onions until mostly smooth and combined, leaving a little texture. Avoid over-mashing, which can make the filling gummy. Divide the mixture into 8 equal portions and let the portions cool slightly until comfortable to handle.
Firmly shape each portion into a compact, oval-shaped patty, pressing out any gaps so it holds together. Arrange on a tray or large plate and refrigerate uncovered for 15 minutes to firm up before breading.
Prepare three shallow plates: one with cornstarch, another with beaten eggs, and the last with panko breadcrumbs. Coat each patty in cornstarch, shaking off the excess. Dip into the beaten eggs, letting the excess drip off, then coat all sides evenly with panko breadcrumbs, gently pressing to help them adhere.
Heat 2 inches of vegetable oil in a deep, heavy-bottomed pot to 325-350°F. Carefully add the croquettes in small batches without overcrowding. Fry for about 3-4 minutes, flipping halfway, until golden brown and crispy. Transfer to a wire rack in a single layer to drain. Allow the oil to reheat between batches.
Serve the crispy korokke immediately with tonkatsu sauce.