Crack the eggs and set the whites aside to beat into stiff peaks. In a mixing bowl, combine the yolks with the sugar, then stir in the mascarpone.
Add the pistachio paste to the mixture with the beaten egg whites.
In a bowl, mix the milk and natural vanilla extract. Dip the cookies in the vanilla milk.
In a baking pan, arrange a layer of sponge cake, followed by a layer of the filling, then a second layer of sponge cake, and repeat until all the filling is used up.
Smooth the surface with a spatula and sprinkle with ground green pistachios.
Let it sit in the refrigerator for at least 3 hours.