Prepare the pork cutlets by gently pounding them with a meat mallet to a uniform 1/2-inch thickness to ensure even cooking. Season both sides of the pork chops lightly with salt and black pepper.

Set up a breading station with three shallow bowls containing the flour, the single beaten egg, and the panko breadcrumbs. Dredge each pork chop in the flour, dip into the egg, and then coat thoroughly with panko, pressing gently so the breadcrumbs adhere in a thick, even layer.

Heat the vegetable oil in a heavy-bottomed skillet over medium-high heat until it reaches 340°F (170°C). Fry the breaded pork cutlets for about 3 to 4 minutes per side, or until they turn a deep golden brown and the meat is cooked through. Transfer them to a wire rack to drain, then slice each cutlet into 1-inch thick strips.

In a small bowl, whisk together the dashi stock, soy sauce, mirin, and sugar until the sugar is fully dissolved. In a separate bowl, lightly beat the remaining two eggs, leaving visible streaks of yolk and white for a classic, marbled texture.

In a small skillet or katsudon pan, combine the dashi mixture and sliced yellow onions, bringing it to a simmer over medium heat. Cook for about 3 to 4 minutes until the onions become tender and slightly translucent.

Place the sliced pork cutlet directly on top of the simmering onions in the pan. Gently pour the beaten eggs over the pork and onions, cover the skillet with a lid, and cook for 1 to 2 minutes until the egg whites are just set but the yolks remain soft and velvety.

Slide the finished katsudon topping carefully over a large bowl filled with warm steamed Japanese rice. Garnish with sliced green onions and serve immediately while the pork remains partially crispy and the dashi broth infuses the rice.