For the dough

• 2 pounds potatoes, russets if baking or yukon golds if boiling
• 2 eggs, lightly beaten
• 1 tablespoon salt
• ½ teaspoon freshly ground black pepper
• 1½ cups all-purpose flour, plus more for kneading

For the filling

• 2 tablespoons olive oil
• 1 onion, minced
• 2 cloves garlic, minced
• ½ pound ground beef
• 1 teaspoon salt
• ½ teaspoon freshly ground black pepper
• 2 tablespoons chopped fresh flat-leaf parsley
• 1 slice rustic bread, crusts removed, soaked in water to cover, and squeezed dry (optional)
• 1 egg, lightly beaten
• 1 egg white, lightly beaten
• vegetable oil for deep-frying
• 1 egg yolk, lightly beaten, if baking pastries

First, make the dough: If baking the potatoes, preheat the oven to 400 degrees F Pierce the potatoes with a fork, place on the oven rack, and bake until very soft, about 1 hour. Remove from the oven and, when just cool enough to handle, cut in half, scoop out the potato flesh, and pass it through a ricer or food mill placed over a bowl. Add the eggs, salt, pepper, and enough of the flour to make a smooth dough that holds together like a gnocchi dough. Start with 1½ cups and knead in more flour if it is too wet. If boiling the potatoes, peel them and place in a saucepan with salted water to cover generously. Bring to a boil and cook until tender, about 30 minutes. Drain well and pass through a ricer or food mill placed over a bowl, or simply mash. Add the eggs, salt, pepper, and flour as directed above. Knead the dough on a lightly floured surface for a few minutes until it holds together and feels a bit elastic but not wet.

While the potatoes cook, make the filling: Warm the olive oil in a sauté pan over medium heat. Add the onion and sauté until tender and translucent, about 10 minutes. Add the garlic and beef and cook, breaking up the meat, until the meat is no longer pink, about 5 minutes. Add the salt, pepper, and parsley and stir well. Cook until meat is browned, about 10 minutes. Remove from the heat and stir in the soaked bread, if using, and the egg. Let the mixture cool.

On a lightly floured surface, roll out the dough ⅓ to ½ inch thick. Using a 3-inch biscuit cutter or glass, cut out rounds. Place a heaping teaspoonful of the meat mixture in the center of each circle. Run a stripe of egg white around the edge, fold in half, and press the edges together, sealing securely.

Pour vegetable oil to a depth of 2 inches into a sauté pan and heat to 350 degrees F on a deep-frying thermometer. When the oil is hot, add the pastries, in batches, and fry, turning once, until golden, about 6 minutes. Using a slotted spoon or tongs, transfer to paper towels to drain. Alternatively, arrange the pastries on an oiled baking sheet, brush the top of each pastry with egg yolk or olive oil, and bake in a 400 degrees F oven until golden, about 30 minutes. Serve the pastries hot.