Preheat your oven to 350F (177C). This is crucial as a well-preheated oven ensures that your cake rises beautifully and evenly.
Prepare a large, 13×18-inch sheet pan by spraying the sides with baking spray and lining the bottom with parchment paper. This will help the cake come out easily after baking.
Add the shelled pistachios to a food processor and pulse until they are coarsely chopped. Set these aside as they will be folded into the batter.
In a large bowl, use an electric hand mixer or a stand mixer to whisk together the eggs, sugar, lemon zest, and vanilla extract on high speed for about 8 to 10 minutes. The mixture should become fluffy and voluminous, almost like a meringue.
In a separate bowl, whisk together the flour and baking powder. This ensures that your dry ingredients are well combined before folding them into the wet mixture.
Now, sift the flour mixture into the egg mixture in three batches, folding gently with a rubber spatula after each addition. This technique helps maintain the fluffiness of the batter.
Measure out 1 cup of the ground pistachios and fold them into the cake batter gently. Be careful not to deflate the mixture.
Transfer the cake batter to the prepared sheet pan, spreading it evenly and leveling the top with an offset spatula for a smooth finish.
Bake in the preheated oven for about 18 to 21 minutes, or until the top is lightly browned and the cake is set. Keep an eye on it!
Once baked, prep your rolling area – have a clean kitchen towel on hand, along with powdered sugar, a wire rack, and a clear countertop. These will be essential for the next steps.
Remove the cake from the oven and carefully run a knife along the edges to loosen it from the pan. This prevents it from breaking apart.
Using a sifter, sprinkle powdered sugar over the top of the warm cake. This will help prevent it from sticking to the towel when you roll it.
Place the clean kitchen towel over the cake, then place a wire rack on top. Invert the cake onto the wire rack and gently peel off the pan and parchment paper.
Once the parchment is off, place the peeled paper back onto the cake. Starting with the short end, very slowly and loosely roll the cake up using the kitchen towel. This rolling method helps shape the cake.
Let the rolled cake cool completely. This step is crucial for the cake to hold its shape when you unroll it later.
In a mixer bowl, add the room-temperature cream cheese and beat it for 4 to 5 minutes until smooth. Remember to scrape down the sides to ensure everything is well mixed.
Add in the chilled heavy cream, vanilla, and powdered sugar. Beat on medium-high speed for about 1 minute until combined.
Stop to scrape down the sides of the bowl, then add the pistachio paste. Continue whisking until stiff peaks form, about 4 to 5 minutes. Keep this frosting chilled until you're ready to use it.
In a shallow bowl, add the raspberries and optional sugar, mashing them with a fork until well combined into a puree.
Very gently unroll the cooled cake on a wire rack. Be careful not to tear it.
Spread the raspberry puree over the cake evenly, making sure to reach all the edges.
Next, spoon about 3 cups of the pistachio whipped cream frosting over the raspberry layer, spreading it evenly to the edges. Avoid overfilling to prevent cracking.
Sprinkle the remaining ground pistachios on top of the frosting layer for added texture and flavor.
Carefully roll the cake back up, just as you did before. Transfer it to a flat platter or serving dish.
Using an offset spatula, frost the outside of the cake generously with the pistachio whipped cream frosting. Sprinkle more ground pistachios on top for decoration.
If you have any remaining frosting, transfer it into a pastry bag and pipe decorative roses on top of the cake. Garnish with fresh raspberries and mint leaves for a beautiful presentation.
Refrigerate the cake overnight before serving, or for at least 10 to 12 hours for the best flavor and texture.
When ready to serve, use a sharp, serrated knife to slice the cake into pieces.