Begin by peeling the potatoes and cutting them into quarters. Place them in a large pot of salted water and bring to a boil. Cook until tender, about 15-20 minutes. Drain and let cool slightly before mashing until smooth. Set aside.
In a skillet over medium heat, add a tablespoon of oil and sauté the onion, green bell pepper, and garlic until softened, about 5 minutes. Add the cooked ground beef (or chicken), cumin, paprika, salt, and black pepper. Stir to combine and cook for another 5 minutes. Remove from heat and mix in the cilantro if using. Let the filling cool.
Once the potato mash is cool enough to handle, take a portion (about 1/4 cup) and flatten it in your palm. Place a tablespoon of the filling in the center and carefully fold the potato around it to form a ball. Repeat with the remaining potatoes and filling.
Set up a breading station: Place the flour in one shallow dish, beat the egg in another, and spread the breadcrumbs in a third. Roll each potato ball in flour, dip in the egg, and coat with breadcrumbs.
In a deep skillet or pot, heat about 2 inches of vegetable oil over medium-high heat. Once hot, carefully add the potato balls in batches, frying until golden brown and crispy, about 4-5 minutes per side. Use a slotted spoon to transfer them to a paper towel-lined plate to drain excess oil.
Serve the papas rellenas warm with your favorite dipping sauce or salsa.