Preheat oven to 300°F (150°C). Place 1 1/4 cup (125 g) raw pistachios on a baking sheet and bring them to the oven to toast for 15 minutes. Let the nuts cool, chop, and set aside for decoration.

Decrease oven temperature to 275°F (135°C). Place four 8 inches (20 cm) cake rings on a baking sheet layered with parchment.

To make pistachio dacquoise, place egg whites with cream of tartar in the bowl of a stand mixer fitted with the whisk attachment. Beat egg whites at medium speed for 1 minute, gradually adding sugar until soft peaks.

Switch the mixer to high speed and whisk the meringue for about 4 to 5 minutes until stiff peaks. Add chopped raw pistachios and gently mix with a rubber spatula until just combined.

Divide the meringue preparation equally into the prepared cake rings and spread evenly with a small spatula. Instead, you can pipe the pistachio mixture as a spiral using a pastry bag fitted with Ateco plain pastry tip 809.

Bake for 1 hour or until lightly golden brown. Let cool for 5 minutes; use a small knife to release the edges of the dacquoise discs, and remove the cake rings. Then, flip each of the discs onto another sheet of parchment paper. Finally, peel off the parchment from the bottom and allow it to cool completely.

To make the buttercream, whip egg yolks at high speed, using an electric mixer or stand mixer, until pale and doubled in volume, for about 8 to 10 minutes.

Bring water and sugar in a heavy-bottomed saucepan over low heat. Cook sugar syrup until it reaches 240°F (115°C): use a cooking thermometer.

Reset the mixer to low speed, and while whisking, pour the hot sugar syrup in thin streams into the beaten egg yolks and beat until the preparation cools down, for about 4 minutes. In a separate mixing bowl, beat the softened butter at low speed until smooth. Increase speed to medium, add the egg yolk/sugar mixture, and then dark rum. Beat until smooth and creamy.

To assemble the cake, place a cake board on a flat surface and dot a little bit of the buttercream filling in the center of the board. Place the first dacquoise disc on the board and gently press to fix it. Spread buttercream on the top of the disc. Sprinkle with chopped pistachios.

Repeat the process with the remaining three discs and the buttercream. Cover the top and sides of the torte with the remaining buttercream using a bent spatula. Sprinkle it all over with chopped toasted pistachios. Refrigerate overnight.