Whisk 1 of the eggs in a medium bowl. Press the potatoes through a ricer into the bowl. Add the Parmesan, butter, chives, parsley, nutmeg, cayenne, salt, and black pepper, to taste. Mix gently with a rubber spatula until evenly combined. Using your hands, form the potato mixture into ovals a bit smaller than the size of an egg, and then flatten slightly. Press a cube of Gorgonzola into the center of the oval and pack the potato mixture around the cheese until it forms a smooth, egg-shaped ball. Continue until all the potato mixture is used up.
Beat the remaining egg in a shallow plate. Put the breadcrumbs in another shallow dish and set it next to the egg. Roll a croquette in the egg until coated, then in the breadcrumbs, and place it on a clean plate. Repeat with the remaining croquettes. Refrigerate for at least an hour.
Pour enough vegetable oil into a heavy-bottomed skillet to reach a depth of 1/4 inch. Heat the oil over medium heat, and fry the croquettes a few at a time, turning, until golden brown, about 4 minutes. Transfer to a paper towel-lined plate and salt to taste. Repeat with the remaining croquettes. Transfer to a serving platter and serve warm.
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