You have two things to contend with before you can make corned beef hash crispy: rendering fat from the beef and water from the potatoes. Moist food doesn't crisp, so before hot oil can brown and caramelize the beef and potatoes, they have to lose their surface moisture. With beef, it's easy -- moisture evaporates from corned beef in minutes. Potatoes, on the other hand, need a few prep tricks and a pressing technique during cooking to make them crispy.
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Picking Proper Potatoes
You can never get starchy potatoes as crispy as waxy potatoes. Potatoes are broadly categorized according to starch content. Waxy, or low-starch potatoes, such as Yukon Gold, don't crisp as well as high-starch potatoes, such as russet, because they hold their shape longer during cooking. Because high-starch potatoes hold their shape longer, the oil has enough time to crisp them before they start to break down, which ultimately results in a crispier, crunchier bite. Waxy potatoes, on the other hand, don't hold their shape well during cooking, causing them to break down faster -- perfect for mashing but not frying. Peel the potatoes and slice them into 1/2-inch cubes or grate them. Rinse the potatoes under cold water and place them in a bowl of water.
Blanching for Bite
Potatoes blanched in water to which an acid has been added before frying always turn out crispier than unblanched potatoes. Blanching expels starch within the potato cells, which leaves more room for them to dehydrate then fill with oil and turn crisp during frying. When the potato cells lose starch during blanching, it doesn't affect their structural strength, but simply makes the conditions more conducive to crisping. Adding a food acid, such as lemon juice or vinegar, to the water lowers its pH -- acidulates it -- which increases the amount of time potatoes can blanch without breaking down. The longer they blanch, the crisper they get when fried. You need 1 quart of water and 1 tablespoon of vinegar to boil 1 pound of diced or sliced potatoes. Blanch potato cubes in boiling water for three minutes; blanch grated potatoes for one minute. Drain the potatoes and dry them with paper towels.
Selecting a Skillet
The only way to cook corned beef hash crispy is to cook it evenly, and the only way to cook it evenly is with a wide, heavy-bottomed stainless steel or cast iron frying pan. You need a wide pan so the hash sits in an even, uniform layer without overcrowding, because overcrowding a pan creates steam and moist food doesn't brown. You need a heavy pan to conduct heat steadily and evenly; thin pans have hot spots that prevent balanced crisping. Heat about 1/4 inch of vegetable oil in the pan over medium heat for five minutes.
Dice the corned beef into 1/4- to 1/2-inch cubes and cook until brown, about five minutes, stirring occasionally. Set the heat to medium-high and add your vegetables -- sliced bell peppers and onions are classic -- and cook until soft, about three minutes. Set the heat to medium-high and add the potatoes. The potatoes lower the pan temperature momentarily, but raising the heat compensates for it. Press the hash into the pan using a spatula and cook until golden brown and crisp, about five minutes. Turn the hash over, press it into the pan with the spatula and cook until the second side crisps, about another five minutes.