Peel and quarter the potatoes and place them in a large saucepan with enough water to cover. Add 1 to 2 teaspoons salt and bring to a gentle boil. Cook the potatoes until tender when pierced with a knife, about 20 minutes. Drain the potatoes and mash them together with the butter and cream cheese. Season the mashed potatoes with salt and pepper to taste. Refrigerate the mashed potatoes until cooled and firm enough to shape with your hands.
Scoop about ¼ cup of the potato mixture into the cupped palm of your hand and use the fingers of your other hand to form it into a shallow bowl shape. Place a rounded tablespoon of the Picadillo Clásico in the hollow and press down on it with your fingertips. Mold the sides up over the filling to enclose it. If necessary, add a little more potato mixture to enclose the filling completely. Repeat until all the potato mixture and filling have been used. Use both hands to shape the stuffed potatoes into balls. As you finish them, place the shaped potato balls on a baking pan and refrigerate until ready to deep-fry.
In a shallow bowl, beat the eggs together with 3 to 4 tablespoons water. Roll the potato balls in the flour, and gently shake off any excess. Dip them into the eggs and then roll them in the bread crumbs until they are evenly coated.
Preheat the oven to 300°F. Line a large baking sheet with slightly crumpled paper towels.
In a deep-fryer or a large, deep skillet, heat at least 2 inches of oil to 375°F. Using a slotted spoon, gently lower a stuffed and breaded potato roll into the hot oil. Fry one at a time, using the spoon to gently turn it, until golden brown on all sides, 2 to 3 minutes. As they are fried, transfer the potato rolls to the baking sheet to drain. Keep them warm in the oven until all are cooked, then serve hot. These may be prepared and fried in advance, then frozen for up to 1 month. To serve, reheat in a 350°F. oven for about 30 minutes, until crisp and hot.