Preheat the oven to 300°F (150°C). Line baking sheets with parchment paper and draw four equal circles as guides.

Beat the egg whites and cream of tartar until soft peaks form. Gradually add the sugar while continuing to beat until stiff, glossy peaks develop.

Gently fold the finely ground pistachios and flour into the meringue mixture.

Work carefully to maintain as much air as possible in the batter. The mixture should remain light and fluffy.

Spread the mixture evenly inside the prepared circles.

Bake for approximately 45 to 60 minutes or until the layers are crisp and lightly golden. Allow them to cool completely before removing from the parchment paper.

In a saucepan, combine sugar and water and cook until a syrup forms.

Beat the egg yolks until pale and gradually add the hot syrup while mixing. Once cooled slightly, beat in the softened butter and vanilla until smooth and creamy.

Place one meringue layer on a serving plate and spread a generous layer of buttercream over the top.

Repeat with the remaining layers until all layers are stacked. Cover the sides and top with the remaining buttercream.

Decorate the cake with chopped pistachios and additional buttercream if desired.

Refrigerate for at least 4 hours before slicing. Serve chilled and enjoy the perfect combination of crisp pistachio layers and silky buttercream.