Place the pistachios into a food processor and pulse until finely ground, being careful not to over-process or it will turn into a paste. In a bowl, combine the ground pistachios with flour, baking powder, and salt. Set aside.
In a large mixing bowl, beat the softened butter and sugar together until the mixture is light and fluffy, about 3 minutes. Add the eggs one at a time, beating well after each addition. Stir in the milk, vegetable oil, vanilla extract, and almond extract gently. Fold in the dry ingredients—the flour and pistachio mixture—until just combined.
Divide the batter evenly into three greased 8-inch round cake pans lined with parchment paper. Bake at 175°C (350°F) for 22 to 25 minutes, or until a toothpick inserted into the center comes out clean. Allow the cake layers to cool completely on a wire rack.
In a chilled bowl, whip the heavy cream until soft peaks form. Add the mascarpone cheese, powdered sugar, and vanilla extract, and continue to beat until the mixture is smooth and thick. Be careful not to overmix. Refrigerate the cream until ready to use.
Place one cake layer on your serving plate and spread a generous amount of mascarpone cream over it. Repeat with the remaining layers. Once stacked, frost the top and sides of the cake with the remaining cream. Press the chopped pistachios onto the sides and sprinkle some over the top for decoration.
Chill the cake in the refrigerator for at least 2 hours before slicing. This resting time allows the flavors to meld beautifully and the cream to firm up.