1- Bring a large pot of salted water to a boil. Cook the unpeeled potatoes until they are tender when pierced with a fork, about 25 minutes. Once potatoes are cooked, drain them in a colander.
2- When they are cool enough to handle, peel and mash the potatoes thoroughly or pass through a potato ricer. Season the mashed potatoes with salt and pepper to taste. Chill the potatoes uncovered for several hours, or overnight.
3- Once the potatoes are very cold, stir the egg into the mashed potatoes until well mixed. Cook the egg in boiling water until hard boiled and set aside.
4- Heat the vegetable oil in a skillet. Add the onions, garlic and aji paste and cook until soft and fragrant, then add the cumin and paprika and cook 2 minutes more, stirring, then add the ground beef and cook until browned.
5- Add the beef broth and the raisins and simmer for 10 to 15 minutes more, or until most of the liquid is gone. Season the mixture with salt and pepper to taste. Remove from heat and let cool.
6- Peel the hard boiled egg and chop it into about 6 pieces. With floured hands, place about ¼ cup of mashed potatoes in one hand, and make a well in the center. Fill the well with 1 to 2 tbsp of the beef mixture and a piece of hard boiled egg.
7- Mold the potatoes around the beef, adding more potato if necessary to fully enclose the filling. Shape into an oblong oval with slightly pointy ends, about the size of a medium potato.
8- Repeat with the rest of the ingredients, you should be able to make 6 croquettes. Coat each papa rellena generously with flour.
9- In a deep skillet, heat 2 inches of oil to 360ºF. Set the oven to 200ºF. fry the potatoes in batches until they are golden brown.
10- Drain them on a plate lined with paper towels. Keep the papa rellena warm in the oven until ready to serve.