Preheat the oven to 300°. In a small skillet, cook the butter over moderately high heat until deep golden brown, about 2 minutes. Remove the skillet from the heat.
In a medium bowl, whisk the flour with the sugar and egg whites until smooth. Whisk in the browned butter and hazelnut oil. Let the batter stand at room temperature for 1 hour.
Line a large baking sheet with a silicone mat. Spoon 6 teaspoons of the batter onto the baking sheet 3-inches apart. Spread the batter into 3 inch rounds. Bake the tuiles in the center of the oven, 2 baking sheets at a time, for 8 minutes, or until light golden, turning the baking sheets halfway through.
Drape the warm tuiles over a rolling pin immediately after removing them from the oven. Return the tuiles to the oven for 30 seconds if they become too brittle to bend. Repeat with the remaining batter.
The tuiles can be stored in an airtight container overnight or frozen for up to a month.