Prepare the shelled pistachios by grinding them in a food processor until finely ground but not pasty. Combine with flour, baking powder, and salt in a bowl.

In a large bowl, cream together softened butter and sugar until light and fluffy, about 3 minutes.

Incorporate eggs one by one, mixing well after each addition. Then add milk, vegetable oil, and vanilla extract, blending until smooth.

Gently fold the dry mixture into the wet ingredients using a spatula until just combined.

Preheat oven to 175°C (350°F). Grease three 8-inch round pans. Divide batter and bake for 22-25 minutes until a toothpick comes out clean.

Whip the heavy cream until soft peaks form. Gradually add mascarpone cheese, powdered sugar, and vanilla, mixing until smooth.

Assemble the cake by stacking layers with mascarpone cream in between, frosting the top and sides.

Refrigerate for at least 2 hours before serving to allow flavors to meld.