In a small bowl, pour 1/4 cup mirin over the onion and let marinate. In a shallow bowl, lightly beat the eggs with 1 teaspoon soy sauce. Place the flour in another shallow bowl; place the panko in another separate bowl.
Coat the pork with the flour, shaking off any excess. Dip the pork slices in the egg mixture, letting the excess drip off, then coat with the panko.
In a large skillet, heat the oil over medium-high heat until rippling. Add the pork and fry, turning once, until golden and crisp, about 5 minutes on each side. Transfer to paper towels to drain.
In a small bowl, stir together the ketchup, remaining 1 tablespoon mirin and 2 teaspoons soy sauce. Add 1 teaspoon water to thin if desired.
Slice the pork. Divide the rice among 4 bowls and top with the pork, sauce and pickled onion.