For the pistachio sponge cake (1 day in advance): Preheat the oven to 170 °C. Whisk the whole eggs with the sugar for 15 to 20 minutes until the mixture triples in volume and forms ribbons.
Mix the pistachio paste with 4 tablespoons of the egg-sugar mixture, then fold the mixture into the batter. Gently fold in the sifted flour without deflating the batter.
Divide the batter between two 20-cm dessert rings, which have been buttered and floured, placed on a baking sheet lined with parchment paper. Bake for 20 minutes without opening the oven. Check for doneness by inserting a knife; it should come out clean. Then let cool completely on a wire rack.
For the vanilla buttercream (1 day in advance): Whip the softened butter, powdered sugar, heavy cream, and vanilla extract for about 2 minutes until the mixture is light and creamy.
Set aside 4 to 5 tablespoons of cream in a piping bag in the refrigerator for decoration, then place the rest in a second piping bag for assembly.
To assemble (one day before serving): Place the first sponge cake layer on the cake stand and spread buttercream over it. Add the second sponge cake layer, then cover the top and sides of the cake with the remaining buttercream. Smooth the surface with an offset spatula and refrigerate overnight.
For decoration (J): Remove the cake from the refrigerator. Warm the reserved piping bag of cream slightly in your hands to soften it, then pipe a thin layer of cream around the edge of the cake.
Cover the sides with rainbow vermicelli, then decorate the top with white meringues and gold candles before serving.
