Preheat the oven to 350°. In a medium bowl, using a handheld electric mixer, cream the butter and granulated sugar until combined. Beat in the egg whites, one at a time. Add the ground almonds, flour and the ground spices and beat at low speed until a soft batter forms.
Line 2 baking sheets with parchment paper. Spoon level teaspoons of the batter onto the prepared baking sheets, about 4 inches apart. Using an offset spatula, spread the batter into 3-inch rounds. Bake until golden, about 10 minutes. Cool for 1 minute, then transfer the tuiles to a rack with a spatula. Cool the baking sheets between batches by running the undersides under cold tap water and drying thoroughly before replacing the parchment. Repeat with the remaining batter.