Preheat your oven to 465°F (240°C) and line a baking sheet with parchment paper, placing 7-inch pastry rings on it.

Grind pistachios in a food processor until finely textured. Combine with powdered sugar and cake flour in a mixing bowl.

Beat egg whites with cream of tartar and salt until foamy, then gradually add granulated sugar and beat until stiff peaks form.

Gently fold the pistachio mixture into the meringue in two additions, ensuring not to deflate it.

Divide the meringue batter into the pastry rings and bake at 350°F (180°C) for about 15 minutes until lightly golden.

Cool the layers in the oven with the door cracked for about 1 hour to prevent cracking.

Beat egg yolks in a bowl until pale. Cook granulated sugar and water to 240°F (115°C) and then drizzle into yolks while whisking.

Incorporate room-temperature butter into the yolk mixture until smooth, then add vanilla extract and pistachio paste.

Assemble the cake by placing one dacquoise layer on a plate, adding buttercream, and topping with the second layer and decorative buttercream.

Allow the assembled cake to sit at room temperature for 20 minutes before slicing and serving.