In a large skillet, heat 2 tablespoons oil over medium heat; add the onion and cook until softened, about 5 minutes. Stir in the turkey, olives, gravy and currants and season with salt and pepper; cook until heated through, 3 to 4 minutes. Let the filling cool.
In a large bowl, combine the flour, baking powder and 1/2 teaspoon salt. Using your fingers, mix in the shortening until crumbly. Using a fork, stir in 5 tablespoons ice water and the whole egg until the dough comes together; transfer to a work surface and knead until smooth. Pat into a disk, cover with plastic wrap and refrigerate for 15 minutes.
Cut the dough into 12 pieces and shape into balls. On a floured work surface, roll each ball of dough into a 5-inch round; top each with 1/4 cup filling. Brush the dough edges with the egg white, fold over and seal (crimp decoratively, if desired). Refrigerate for at least 15 minutes or up to overnight.
In a large cast-iron skillet, heat the remaining oil over medium-high heat (a pinch of flour should sizzle immediately when dropped in). Working in batches of 3, add the empanadas and fry, turning once, until golden, about 3 minutes. Using a slotted spoon, transfer to paper towels to drain. Let cool for 5 minutes before serving.