Using about 1/4 cup stiff, cold mashed potatoes, form into a ball.
Flatten ball and make a hollow.
Put about 1 tablespoon picadillo inside indentation.
Enclose meat in potatoes, forming into a ball. Place on baking sheet.
Repeat with remaining potatoes and meat.
Roll each ball in egg mixture then in breading. Place on baking sheet. Chill 2 to 4 hours.
Heat oil in a deep-fat fryer or deep frying pan. I used a deep frying pan and about 1 1/2 inches of oil. When oil is hot, carefully place 2 or 3 balls in pan, using a slotted spoon and turn until golden brown on all sides, 2 or 3 minutes. Transfer to clean baking sheet lined with paper towels.
Hold in warm oven until all papas are fried. Makes approximately 2 dozen, depending on the size.