Remove the puff pastry from the freezer and let it thaw on your countertop.
Heat the oil in a medium casserole or a sauté pan set over medium heat. Once hot, cook the onion for 3 to 4 minutes until it softens. Incorporate the mushrooms, sprinkle in the salt and pepper, and cook for another 5 to 6 minutes, until the juices come out and they begin to dry out, and the mushrooms start browning a bit. Add the tomatoes and cook for 6 to 7 minutes, until they start breaking down and becoming mushy and soft. Add the olives and jalapeños, mix well, and cook for another minute.
Remove from the heat, add the sardines, combine well and set aside.
Separate the egg whites from the egg yolks in two small bowls. Use a fork or a whisk to beat them separately.
Place the racks in the lower and upper thirds of the oven. Preheat the oven to 400 degrees Fahrenheit. Line a couple of baking sheets with parchment paper.
Lightly sprinkle flour on the countertop and rub some on the rolling pin. Roll out the puff pastry to thinner than 1/4-inch and use a 4-to-5-inch round mold to cut circles. Add a generous tablespoon of the sardine filling in the middle of each round. Brush a bit of the beaten egg white around the edges each round. Fold each one into a half moon shape and press the sides.
Using a fork, press the side of the empanada to help seal and decorate it. Brush the egg yolk on top of the empanadas and place them on the prepared baking sheets. Place the empanadas in the oven. Bake anywhere from 20 to 22 minutes, until the tops of the empanadas have puffed and are a shiny golden brown.