Bring a large pot of water to a boil. Add the cubed potatoes and boil for 10 to 12 minutes, until just fork-tender but not falling apart (larger cubes may need the extra minute or two).
Drain the potatoes well, pat them dry with paper towels, and set aside.
In a large skillet over medium-high heat, melt the butter. Add the diced onion and cook for 3 to 4 minutes, stirring occasionally, until softened and translucent.
Stir in the minced garlic and cook for 1 minute, or until fragrant. Season with the kosher salt and black pepper.
Add the cubed corned beef and boiled potatoes to the skillet. Gently stir to combine, then lightly press the mixture down into an even layer.
Cook undisturbed for 6 to 7 minutes, allowing the bottom to develop a nice golden-brown crust.
Flip sections of the hash and continue cooking for 10 to 15 more minutes, turning occasionally with a spatula to brown evenly on all sides. (For maximum crispiness, resist stirring too often.)
Remove from heat, garnish with chopped fresh parsley, and serve warm. Top with fried eggs and toast for the classic experience.