Begin by grinding shelled pistachios in a food processor until finely chopped, but avoid creating a paste. In a mixing bowl, combine the ground pistachios with all-purpose flour, baking powder, and salt, whisking them together to ensure an even distribution of these dry ingredients.

In another mixing bowl, beat softened unsalted butter and granulated sugar using an electric mixer until the mixture is light and fluffy, about 3-4 minutes. Gradually add eggs, one at a time, mixing well after each addition, then incorporate the whole milk, vegetable oil, and vanilla extract. Carefully fold in the dry mixture until just combined.

Preheat your oven to 175°C (350°F). Grease three 8-inch round cake pans liberally with butter and dust with flour. Evenly divide the batter among the prepared pans and bake for 22-25 minutes or until a toothpick inserted into the center comes out clean.

While the cake layers cool, prepare the frosting. In a chilled mixing bowl, whip heavy cream until soft peaks form. Gently fold in the mascarpone cheese, powdered sugar, and vanilla extract until smooth.

Once your cake layers are completely cool, place one layer on a serving plate. Spread a generous layer of mascarpone cream on top, then add the second layer of cake and repeat. Place the final layer on top and frost the top and sides of the entire cake.

After assembling, refrigerate the cake for at least 2 hours before serving. Garnish with additional chopped pistachios before serving.