Bring a large pot of salted water to a rapid boil, then add peeled, diced potatoes. Cook until they’re fork tender, but not mushy. Drain.
While the potatoes are cooking, place corned beef in a food processor fitted with blade attachment. Pulse several times until the beef is finely chopped. Alternatively, you can cut the corned beef into a fine dice.
Heat unsalted butter in a large skillet over medium heat. Add diced onion, season with kosher salt, then cook, stirring occasionally, until softened.
Add Ketchup, the remaining kosher salt, and black pepper. Stir until well mixed, then cook.
Use a thin metal spatula to carefully flip the hash over. Cook, then garnish with a tablespoon of freshly chopped parsley. Enjoy immediately with poached eggs!