Preheat the oven to 400 degrees.
Place the pieces of parchment paper on a flat surface, fold them in half crosswise, and cut each piece like a large paper heart cutout. Open the fold flat and place each fillet lengthwise just to the right of the fold. On each fillet, sprinkle ½ teaspoon salt, ¼ teaspoon pepper, 1 tablespoon olive oil, 1 tablespoon lemon juice, and 2 sprigs of thyme, and place 2 olives alongside the fish.
Brush the edges of the entire parchment paper with the egg whites. Fold the left side of the parchment paper over the right side so the edges line up, creating a packet. Press the edges together to create a seal. Starting at the edge at the top of the heart, make overlapping folds in the parchment, until you reach the “tail” of the heart. Fold the last end underneath to seal the packet. Place all the packets on sheet pans, making sure the oil and lemon juice don’t run out when you transfer them. Bake for 15 minutes exactly. Place each packet on a dinner plate, cut an X in the middle with scissors, and serve hot, allowing each person to tear open the packet.
make it ahead: Prepare the packages and refrigerate for up to 1 day. Bake before serving.
Copyright 2012, Make It Ahead, Clarkson Potter/Publishers, All Rights Reserved.