In a pot of boiling water, cook the potatoes until nearly tender, about 14 minutes, then drain, return to the pot, and let the potatoes cool and the remaining liquid evaporate.
Beat the egg whites in a bowl until foamy. In another bowl, mix the bread-crumbs with salt and pepper to taste, the paprika, and the cheese.
Coat the potatoes in egg whites and then in the breadcrumb mixture. Coat again in the egg whites and the breadcrumb mixture. Keep in the fridge until ready to fry.
In a heavy pot, heat 2 inches (5 cm) oil to 350°F (180°C).
Deep-fry the potatoes in batches until they are golden brown and heated through, 3 to 5 minutes, depending on their size. Let them drain on paper towels.
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