Preheat your oven to 225°F (110°C). Beat the egg whites until soft peaks form, then gradually add granulated sugar and whip until stiff peaks form. Gently fold in finely ground pistachios, powdered sugar, salt, and cake flour until just combined.

Line two baking sheets with parchment paper. Using a piping bag, pipe the meringue into 7-inch circles on the parchment, smoothing any imperfections.

Bake for about 1 hour and 15 minutes, until crisp and lightly golden. Turn off the oven, crack the door open, and let cool inside for 30 minutes.

In a saucepan, combine egg yolks, water, and granulated sugar. Cook until sugar dissolves. Whip with a stand mixer on high until pale and thick, about 5 minutes.

Gradually add unsalted butter to the whipped egg yolks, mixing well after each piece. After completely incorporated, add pistachio paste and salt, beating until fluffy.

Assemble the cake by placing one meringue layer on a plate, spreading pistachio buttercream on top, then stacking another layer. Chill in the refrigerator for at least 30 minutes.

Let the cake sit at room temperature for 20 minutes before serving. Optionally, garnish with extra pistachios or fresh berries.