Preheat the oven to 350 degrees F. Bring a small saucepan of water to a boil, drop in the tomato and boil 30 seconds. Remove with a slotted spoon and let cool 5 minutes, then peel and puree in a blender until smooth; set aside.
Heat the vegetable oil in a large sauté pan over medium-high heat. Add the beef and cook, breaking it up with a wooden spoon, until browned, about 7 minutes; season with 1/2 teaspoon salt. Add the onion, carrot, olives, raisins and the pureed tomato. Simmer until thick, about 2 minutes, then remove from the heat and set aside.
Beat the egg with 2 teaspoons water in a small bowl; set aside. Coat a baking sheet with cooking spray. Working with 1 sheet of puff pastry at a time, unfold on a lightly floured surface. Roll out the dough into a 10-inch square, about 1/4 inch thick, using a floured rolling pin. Cut into four 5-inch squares. Place 1/4 cup of the picadillo mixture in the center of each square. Brush the edges with the egg wash and fold diagonally to form a triangle. Crimp the edges with a fork.
Transfer the empanadas to the prepared baking sheet and brush with the remaining egg wash. Bake until golden brown, about 25 minutes.
Photograph by Carol Von Zumwalt