Preheat your oven to 200°F (90°C). In a mixing bowl, whip the egg whites until foamy. Gradually add sugar, beating until stiff peaks form, then gently fold in ground pistachios.

Line two baking sheets with parchment paper, spread meringue onto them in thin layers, and bake for 1.5 to 2 hours until crisp and dry.

Beat softened French butter until creamy, gradually sift in powdered sugar, then add vanilla extract and beat until light and fluffy.

Layer meringue and buttercream on a serving plate, stacking and coating the exterior with remaining buttercream.

Refrigerate the assembled cake for 30 minutes. Slice and serve at room temperature for best enjoyment.