Preheat your oven to 465°F (240°C) and prepare baking sheets with parchment paper and pastry rings.

Combine the pistachios, powdered sugar, and cake flour in a food processor. Pulse until finely ground, but do not turn it into a paste.

Whip the egg whites with cream of tartar and salt until foamy. Gradually add granulated sugar and beat until stiff peaks form (4-5 minutes).

Gently fold the pistachio mixture into the whipped meringue, maintaining the meringue's airiness.

Divide the batter between prepared pastry rings and bake at 350°F (180°C) for about 15 minutes. Cool in the oven for 1 hour.

Make the buttercream by beating yolks until thick. Heat water and sugar until simmering, and pour into yolks while mixing.

Once cooled, add room temperature butter gradually until smooth. Mix in vanilla extract and optional pistachio paste.

Assemble the cake by stacking the dacquoise layers and spreading buttercream in between. Finish with buttercream and chopped pistachios on top.