Add the butter to a large 12” to 14” cast-iron skillet over medium-low heat and add onions to lightly caramelize, which takes about 10 minutes.: As the butter melts it should foam gently and spread a warm glossy sheen across the pan surface, releasing a subtle nutty scent, then add the diced onion so it softens and gradually sweetens. You want to listen for a low steady sizzle, not a violent pop, and watch the edges of the onion transition from translucent to pale gold; this slow color change concentrates flavor and avoids bitter burnt notes. Stir occasionally to ensure even coloring, and if the pan begins to brown too quickly, reduce the heat slightly to maintain gentle caramelization. A common mistake is turning up the heat to rush the process which results in unevenly browned pieces that taste scorched rather than sweet.
Next, add in the garlic and sauté for 30 to 45 seconds or just until fragrant.: When you add the finely minced garlic , the aroma should pop almost immediately, filling the kitchen with a bright, savory perfume while the sizzling sound becomes more lively for the brief period it cooks. Keep the movement quick and light, tossing so the garlic coats the softened onion and heats through, but do not leave it unattended because garlic can go from fragrant to bitter in a breath; the color should remain pale, not brown. This short step builds an aromatic backbone and prevents the dish from tasting flat. Avoid the error of cooking the garlic too long which will introduce an acrid edge to the hash.
Add in the beef and potatoes and pan roast over medium heat for 12-15 minutes or until the potatoes are browned and cooked through. Stir every 1 to 2 minutes.: As you introduce the chopped corned beef and diced potatoes , the skillet noise will deepen into a steady, robust sizzle as moisture evaporates and starches brown, creating a toasty, savory aroma. Let the mixture sit for short periods to form crisp patches, then stir to expose more surface area, aiming for an overall golden mosaic with some darker caramelized bits for texture contrast. The goal is tender potato centers with crunchy edges, and the browning adds complex, almost nutty flavors that contrast beautifully with the salty meat. A frequent slip is stirring constantly which prevents crust formation; instead allow small intervals of undisturbed contact with the pan to develop desirable crispness.
Finish with salt, pepper, chives, parsley, and rosemary. Keep warm.: At this point the kitchen should smell herbaceous and savory, and sprinkling the minced chives , parsley , and rosemary will release bright green notes that lift the dish from rustic to nuanced. Add coarse salt sparingly because the corned beef already contributes salt, and grind fresh cracked pepper over the top for immediate aromatic heat. Toss gently to distribute the herbs while preserving their color and fresh scent, then lower the heat to keep warm without further browning. One mistake to avoid is adding the herbs too early which causes them to wilt and lose vibrancy, muting the final flavor lift.
Serve with your desired type of cooked eggs.: When you plate, the sound of a runny egg yolk breaking over the hot hash is part of the satisfaction, as the glossy yolk blends into the browned nooks and rounds out the saltiness with creamy richness. Choose a method of cooking eggs that complements the texture you prefer, whether it is fried with crisped edges or soft poached for silky contrast, and place them on top or to the side so each bite combines components as you like. A key tip is to time the eggs so they finish hot, because cold eggs can dull the dish; avoid overcooking the yolk if you want that luscious sauce effect.