The tuile batter can be made a day in advance. Refrigerate it in an airtight container until you're ready to bake.
- 1 stick (8 tablespoons) unsalted butter, softened
- 2/3 cup packed light-brown sugar
- 4 large egg whites, room temperature
- 1 cup all-purpose flour
- Pinch of salt
- 1 teaspoon pure vanilla extract
Preheat oven to 350 degrees; with rack in middle. Put butter and brown sugar in the bowl of an electric mixer fitted with the paddle attachment. Mix on medium until fluffy, 2 to 3 minutes. Mix in egg whites, 1 at a time. Mix in flour, salt, and vanilla.
Line a baking sheet with a Silpat baking mat or parchment paper. Spoon 2 tablespoons batter onto the baking mat. Using an offset spatula, spread batter into a 7-inch circle, with the edges slightly thicker than the center. Repeat, making a second circle on the mat.
Bake, rotating sheet halfway through, until edges of cookies turn golden, about 9 minutes. Using a small spatula, immediately transfer 1 cookie to a small bowl (about 5 1/2 inches in diameter and 3 inches deep). Gently mold the warm cookie to the shape of the bowl, pressing bottom down to flatten. Let stand in bowl 30 seconds; remove. Repeat with remaining cookie. If cookies become too cool to shape, return them to oven for 20 seconds. Repeat, baking remaining batter and forming into bowls. If using just 1 baking sheet, let it cool before spreading the next batch of batter onto it.