In a medium bowl, whisk the sugar with the egg whites, butter, flour and green-tea powder until smooth. Cover the batter and refrigerate for 1 hour.
Preheat the oven to 325° and line a baking sheet with a silicone mat. Have a coffee mug and standard-size muffin tin handy. Spoon two 2-tablespoon-size mounds of batter onto the baking sheet, 6 inches apart. Using an offset spatula, spread the batter to make two 6-inch rounds.
Bake in the center of the oven for 12 to 14 minutes, until the edges are browned and the centers are still light. Let cool for 10 seconds, then using a spatula, invert one tuile and place a paper fortune in the center. Fold the tuile in half and then bring the ends together, using the rim of the coffee mug to make the crease. Set the fortune cookie in a muffin cup to hold its shape. Repeat with the second tuile. If the tuile hardens, return it to the oven for a few seconds. Repeat with the remaining batter and fortunes. Let the cookies cool completely before serving.