Step 1: In a large skillet over low heat, melt the butter. When it begins to foam, blend in the flour, then gradually whisk in the milk until the mixture thickens into a smooth paste. Immediately add the ham, salt, pepper, nutmeg, lime juice, and parsley. Continue cooking over low heat for 2 minutes, stirring constantly with a wooden spoon. Remove from heat.
Step 2: Spoon the mixture into a pan or platter and let it cool thoroughly. If made in advance, refrigerate after it reaches room temperature.
Step 3: Sprinkle a light layer of bread crumbs on a work surface. Scoop up 1 tablespoon of the cooled ham mixture and shape it into a cylinder about 1 1/2 inches long and 3/4 inch diameter. Dip it into the beaten egg and then into the crumbs. Repeat with the rest of the mixture, adding more bread crumbs as necessary. If preparing in advance, you can stop at this point and refrigerate, covered.
Step 4: Preheat the oven to 250 F. In a large, heavy-bottomed skillet or deep fryer, heat 2-3 inches of oil to 375 F, or until a drop of the mixture sizzles when it hits the oil.
Step 5: Fry 5-6 croquettes at a time until golden on all sides, turning with a slotted spoon. Don't overcrowd the pan, or the temp will drop and you'll get soggy croquettes. Don't want that!
Step 6: Transfer the croquettes to a paper-towel lined platter to drain, and keep warm in the oven until you've finished with all the croquettes.
Step 7: Serve with lime wedges. Everyone sprinkles lime juice to their taste.
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