Preparation
Begin by preheating your oven to 350°F (175°C). Line the bottoms of three 6-inch cake pans with parchment paper and set them aside.
Grind the Pistachios
Place the shelled pistachios in a food processor or bullet blender and pulse for about 30 seconds until they reach a coarse flour-like texture. Transfer the ground pistachios to a medium-sized bowl.
Make the Dry Mixture
To the bowl with the pistachios, add the all-purpose flour, baking powder, baking soda, and salt. Stir the ingredients together until fully combined and set the mixture aside.
Prepare the Wet Mixture
In a large mixing bowl, whisk together the melted butter and granulated sugar until well blended. Add the eggs one at a time, whisking after each addition until fully incorporated.
Continue the Wet Mixture
Add in the Greek yogurt, light-tasting oil, and vanilla extract. Whisk the mixture again until smooth and combined.
Combine Wet and Dry Ingredients
Using a fine-mesh sieve, sift the pistachio-flour mixture into the wet ingredients to break up any clumps. Any larger pistachio pieces that remain in the sieve can be added back to the batter. Whisk everything together just until combined—avoid overmixing.
Fill the Cake Pans
Evenly distribute the batter between the three prepared cake pans (approximately 320g of batter per pan). Give each pan a gentle spin on the countertop to help spread the batter evenly and encourage flat baking.
Bake the Cake Layers
Bake the layers for about 30–35 minutes, or until the tops are lightly golden and a toothpick inserted into the center comes out mostly clean.
Cool and Release the Cakes
Let the cakes cool in their pans until they’re safe to handle. Run an offset spatula around the edges of each cake, then carefully invert them onto a wire rack. Peel off the parchment paper and allow the layers to cool completely.
Raspberry Jam
In a small saucepan, combine the raspberries, granulated sugar, and water. Cook over medium heat until the mixture reaches a boil, stirring occasionally. Continue cooking until it thickens to a jam-like consistency. When a spatula is dragged through, the jam should part and then slowly come back together.
Strain the Jam
Push the hot jam through a fine-mesh sieve to remove the seeds. Discard the seeds and allow the seedless raspberry jam to cool completely.
Raspberry Buttercream
In the bowl of a stand mixer fitted with the paddle attachment, beat the softened butter on medium-high speed for about 10 minutes, scraping the sides of the bowl halfway through. The butter should become very pale and creamy.
Whip the Buttercream
Add the powdered sugar and start mixing on low speed. Gradually increase to medium-high speed and beat for 5 minutes. Add the cooled raspberry jam and vanilla extract. Slowly pour in the heavy cream, one tablespoon at a time, mixing until you reach a smooth consistency. Scrape the bowl and beat for another 5 minutes until fully whipped.
Soften the Buttercream
Scoop a large spoonful of buttercream into a small bowl and microwave it for about 10 seconds until partially melted. Stir this back into the remaining buttercream to smooth it out. Repeat this step if the buttercream becomes too stiff while decorating.
Prepare to Assemble
Transfer about one-quarter of the buttercream into a piping bag and snip off the tip.
Assemble the Cake – First Layer
Place the first cake layer on a turntable. Pipe a ring of buttercream around the edge of the cake and spoon about 4 tablespoons of raspberry jam into the center. Use an offset spatula to spread the jam evenly within the buttercream border.
Add the Second and Third Layers
Place the second cake layer on top and repeat the process of piping a buttercream ring and spreading raspberry jam inside. Top with the final cake layer.
Apply a Crumb Coat
Spread a thin layer of buttercream over the entire cake to seal in the crumbs. Use a cake scraper to smooth the surface, then refrigerate the cake for about 15 minutes, or until the crumb coat is firm.
Final Frosting Layer
Apply about three-quarters of the remaining buttercream around the cake and smooth it out using a cake scraper to achieve a clean finish.
Decorate
Fill piping bags fitted with your favorite piping tips with the remaining buttercream. Decorate the cake as desired, then finish with a sprinkle of crushed pistachios on top and optional ribbon bows for an elegant presentation.