Preheat and Prepare: Start by preheating your oven to 350°F (175°C). Grease and line three 8-inch round cake pans with parchment paper for easy release and cleanup.
Whisk Dry Ingredients: In a bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt.
Cream the Butter Mixture: Using a mixer, cream the unsalted butter, vegetable oil, and granulated sugar for about 2 minutes until light and fluffy.
Incorporate the Eggs: Add in the large eggs, vanilla extract, and almond extract (if using). Beat the mixture until it’s well combined.
Alternate the Dry and Wet Ingredients: Gradually add half of your flour mixture, followed by half of the buttermilk. Alternate until everything is just combined.
Add Ground Pistachios: Fold in the ground pistachios and, if desired, a few drops of green food coloring.
Bake the Layers: Divide the batter evenly among the prepared pans. Bake for 25-30 minutes.
Cool the Cakes: Allow the cakes to cool in the pans for about 10 minutes, then invert them onto a wire rack to cool completely.
Cook the Jam: In a saucepan, combine the raspberries, sugar, and lemon juice. Bring to a boil.
Thicken the Jam: Dissolve the cornstarch in a bit of water, then stir it into the pan. Cook until it thickens.
Heat the Cream: In a bowl, combine heavy cream and pistachio paste. Heat until hot but not boiling.
Make the Ganache: Pour this hot cream over white chocolate, allowing it to melt. Strain and whisk until smooth.
Beat the Butter: Beat the softened unsalted butter until fluffy, about 3 minutes.
Add Sugar and Ganache: Gradually mix in powdered sugar and cooled pistachio ganache. Beat until light and fluffy.
Layer the Cakes: Place one cooled cake layer on your serving plate, pipe a ring of buttercream, and fill with raspberry jam and ganache.
Repeat the Layers: Top with another cake layer and repeat the filling process. Add the final layer, frosting the top and sides with remaining buttercream.
Decorate: Finish with fresh raspberries and chopped pistachios.