Preheat your oven to 200°F (95°C) and line two baking sheets with parchment paper. In a clean mixing bowl, whip 5 large egg whites with ⅝ cup granulated sugar and 1 teaspoon of cream of tartar until stiff peaks form, which should take around 8-10 minutes. Gently fold in 1¼ cups of finely chopped pistachios and ½ cup powdered sugar mixed with ⅓ cup cake flour until just combined.

Using a piping bag or a resealable plastic bag with a corner snipped, pipe the meringue mixture onto the prepared parchment into two 7-inch circles. Bake the meringue layers in your preheated oven for about 1 hour, or until they feel dry and crisp to the touch. Keep the oven door slightly ajar with a wooden spoon during the last 10 minutes to prevent excess moisture. Once baked, let them cool completely on a wire rack.

In a small saucepan, combine ¾ cup granulated sugar with ⅓ cup water and bring to a simmer over medium heat to create a sugar syrup. Meanwhile, in a mixing bowl, whisk together 8 large egg yolks until pale and slightly thickened. Once the syrup reaches 240°F (115°C), slowly drizzle it into the egg yolks while whisking continuously. Beat until the mixture cools to room temperature.

Gradually add 2½ sticks of room temperature unsalted butter to the cooled egg yolk mixture, beating on medium speed until smooth and creamy. Stir in 1 teaspoon of vanilla extract, 4 tablespoons of pistachio paste, and ¼ teaspoon of salt, mixing until everything is well blended and you have a luxuriously smooth buttercream.

To assemble your Pistachio Dacquoise Cake, place one meringue layer on a serving platter. Spread a generous layer of pistachio buttercream on top, then carefully place the second meringue layer over the buttercream. Repeat for additional layers, ensuring even distribution of buttercream between each meringue layer, creating an elegant and towering cake.

Once assembled, cover the cake loosely with plastic wrap and refrigerate it for at least 2 hours. Chilling enhances the textures, allowing the flavors to meld beautifully while ensuring each slice holds its shape when served. Once chilled, your stunning Pistachio Dacquoise Cake is ready to impress your guests!