Mix the water, vinegar, and salt in a small bowl. Put the flour, baking powder, and water mixture in a food processor, and blend. Drizzle 3 tablespoons of the olive oil in while the processor is running, and blend for 1 minute.
Remove the dough from the food processor, and lay it out on a work surface that has a light dusting of flour. Knead for 2 minutes, then wrap it in plastic wrap, and put in the fridge for 1 hour.
While the dough is resting, prepare the filling. Peel and chop the potatoes. Put them in a pot covered with water, and boil for 15 minutes or until they are tender. Then, drain and add them into a large bowl.
While the potatoes boil, dice the onion, and add it to a frying pan with 1 tablespoon of oil. Cook over medium heat for 10 minutes, stirring frequently.
Mash the potatoes, and add the remaining ½ teaspoon of salt. Add the cooked onions to the bowl with the potatoes, and stir to combine.
Preheat the oven to 375 F. Place the dough on a lightly-floured surface, and roll it out in a rectangle that's ⅛-inch thick.
Using a glass or cookie cutter that is 4 inches inn diameter, cut out 12 dough circles.
Add 1 ½ tablespoons of the filling to the center of the dough circle, then fold all the sides up over the filling, and twist to seal. Brush with the beaten egg, and bake for 25 minutes, or until the tops are golden brown.