Peel, boil, and cube the potatoes in salted water for 20 minutes. Drain and mash, adding butter, egg, corn meal, and ½ tsp. salt. Mix well and refrigerate until the potatoes are cold.
Divide the potatoes into 10 portions. Sprinkle corn meal on one hand and carefully spread one of the potato portions on your hand flattening it in the middle. Take a tablespoon of prepared picadillo and place it in the middle carefully folding the sides over the meat until it is completely sealed. Sprinkle a bit more corn meal on the relleno to form a very thin coat.
Fry over medium high heat until golden.