Preheat your oven to 350°F (175°C). Line three 6-inch round cake pans with parchment and grease the sides.

Pulse unsalted pistachios until coarse flour in a food processor. Combine with flour, baking powder, baking soda, and salt in a bowl.

Whisk melted butter and sugar in a bowl, add eggs one at a time, then Greek yogurt, oil, and vanilla until smooth.

Sift dry mixture into wet ingredients and whisk gently until combined, ensuring not to overmix.

Divide the batter among prepared pans, smooth tops, and bake for 30-35 minutes until golden and a toothpick comes out clean.

Cool cake layers in pans for 10 minutes, then transfer to wire racks to cool completely.

Prepare raspberry jam in a saucepan over medium heat; combine raspberries, sugar, and water, cooking until thickened.

Beat softened butter until creamy, gradually add powdered sugar and cooled raspberry jam, mixing until smooth.

Assemble the cake with one layer on a serving plate, spread jam and buttercream between layers, finishing with the top layer.

Chill crumb-coated cake for about 30 minutes, then apply a thicker layer of buttercream for a polished finish.

Decorate with leftover buttercream and crushed pistachios, creating an appealing centerpiece.