How to Make It
Preheat the oven to 325°. Line 3 baking sheets with parchment paper. In a medium bowl, using an electric mixer, cream the butter with the honey. Beat in the 1/4 cup of confectioners' sugar and the flour, then add the egg white and beat until smooth. Spoon 5 well-rounded teaspoons of batter onto each of the prepared baking sheets, about 4 inches apart. Using an offset spatula, spread the batter evenly into 3- to 3 1/2-inch rounds. Bake the tuiles for about 12 minutes, until they are lightly browned, shifting the baking sheets from top to bottom and front to back for even baking. Transfer the tuiles to a rack and let them cool until crisp. Repeat with the remaining batter to make about 5 more tuiles.
In a small bowl, sprinkle the gelatin over 1 tablespoon of the water and let stand until softened, about 5 minutes. In a blender, puree the blackberries with the remaining 2 tablespoons of water. Strain the blackberry puree into a small saucepan; there should be about 3/4 cup. Add the sugar and bring to a boil. Simmer the blackberry mixture over moderate heat, stirring occasionally, until it is slightly reduced, about 5 minutes. Stir in the softened gelatin until dissolved. Let the mixture cool.
In a medium bowl, using an electric mixer, beat the egg white until firm peaks form. Using a rubber spatula, fold in the cooled berry puree until no streaks of white remain. In another bowl, beat the heavy cream until softly whipped. Fold the whipped cream into the berry mixture and refrigerate until chilled, about 1 hour.
In a small saucepan, combine the water and sugar and bring to a boil. Remove from the heat. Add the lemon verbena and lemon zest and let stand for 30 minutes. Strain the syrup into a cup. Wipe out the saucepan and return the syrup to it. Add the blackberries to the syrup and bring to a boil. Reduce the heat to low and cook, crushing the blackberries against the side of the pan, until the liquid is slightly reduced and the berries have broken down, about 15 minutes. Strain the syrup into a heatproof cup without pressing. Refrigerate the syrup until chilled.
Place 8 tuiles on a work surface. Scoop a slightly rounded 1/4-cup mound of mousse onto each tuile. Stack one mousse-topped tuile on another to make 4 stacks. Top each stack with a plain tuile and press lightly to flatten each stack slightly (in case of breakage, use one of the extra tuiles). Dust the tops with confectioners' sugar. Using a metal spatula, carefully transfer each napoleon to a plate. Garnish with blackberries, drizzle with the berry-verbena syrup and serve at once.