In a small saucepan, warm the butter, sesame oil, orange juice, orange zest, and sugar over low heat until melted and smooth. Remove from the heat and stir in the flour, almonds, and white and black sesame seeds. Let the batter rest for 1 hour at room temperature.
Preheat the oven to 375°F. Line 2 baking sheets with parchment paper. (Don't use silicone baking mats because the cookies may be difficult to remove.) Set a rolling pin for shaping the tuiles on a folded dish towel to steady it and have ready a wire rack.
Drop level tablespoons of batter on the prepared baking sheets, placing only 4 on each sheet and spacing them evenly apart. Slightly flatten the batter with dampened fingers.
Bake one sheet at a time, rotating the baking sheet midway during baking, until the cookies are evenly browned, 8 to 9 minutes.
Let cool briefly, about 1 minute. Using a metal spatula, lift each cookie off the baking sheet and drape it over the rolling pin. (If the cookies cool and harden before you have time to shape them, they can be softened by putting them back in the oven for 30 to 45 seconds.) Let cool on the rolling pin, then transfer the tuiles to a wire rack. Repeat with the remaining batter.
Serve the tuiles within a few hours of baking.
The batter can be made up to 1 week in advance and stored in the refrigerator. You can store the baked tuiles in an airtight container until ready to serve later the same day.
Reprinted with permission from Ready for Dessert: My Best Recipes by David Lebovitz, copyright © 2010. Published by Ten Speed Press, a division of Random House, Inc.