For the cake: Preheat the oven to 350 degrees F. Spray three 8-inch cake pans with nonstick cooking spray.
In a stand mixer fitted with the paddle attachment, cream the sugar, pistachios, butter and salt on medium speed. Add the eggs, one at a time, beating well after each addition. Mix in the vanilla.
Add the flour and baking powder and mix on low speed until smooth. Pour into the prepared cake pans and bake until a tester inserted in the center comes out clean, 20 minutes. Cool the cakes in the pans on racks for 10 minutes, then invert onto the racks and cool completely.
For the blackberry compote: Combine the blackberries, sugar and lemon juice in a saucepan. Bring to a boil over low heat. Let cool.
For the buttercream: Combine the sugar and 3/4 cup of the water in a pot and bring to a boil. Combine the cornstarch with the remaining 1/4 cup water in a small bowl and add to the boiling sugar mixture. Combine the white chocolate chips and vanilla in a large heatproof bowl. Pour the boiling sugar mixture over the white chocolate chips and mix well. Let cool to room temperature.
Pour the melted chocolate mixture into the bowl of a stand mixer fitted with the whisk attachment. Add the butter and mix on low speed until incorporated, then mix on medium speed until light and fluffy. Add the cream cheese and mix until combined.
To assemble: Place a cake layer, top-side up, on a cardboard disc. Pipe a 1-inch border of buttercream around the top and fill in with 2 scoops of buttercream. Spread 1 scoop of blackberry compote evenly on top. Stack the second cake layer, top-side down and repeat with the buttercream and compote. Set the final cake layer, top-side down, on top. Frost the top and sides of the cake with buttercream.
This recipe was created by a contestant during a cooking competition. It has not been tested for home use.