Preheat the oven to 350°F (175°C). Grease a 9×9 inch light metal baking pan and line it with parchment paper.

Add the pistachios to a food processor and pulse until finely ground. Set aside for later use.

In a medium bowl, whisk together the all purpose flour, baking powder, baking soda, and salt. Then set aside the flour mixture.

Add the sugar and lemon zest to a large bowl. Rub the lemon zest and sugar together with your fingertips to extract the most lemon flavor from the zest.

Add in the softened butter. Cream the butter, sugar and lemon zest together with an electric mixer on high speed for 1-2 minutes until light and fluffy.

Then add in the eggs and vanilla and mix on medium speed until pale in color and smooth, about 1 minute.

Add the buttermilk and the dry ingredients to the wet ingredients a little at a time, mixing on low speed until the cake batter is combined. Scrape the sides of the bowl with a rubber spatula as necessary.

Fold in the ground pistachios.

Pour the batter into the prepared baking pan.

Bake the cake for 38-42 minutes, or until a toothpick comes out clean from the center.

Let the cake cool in the pan on a wire rack for 30 minutes, then pull up on the parchment paper to release it from the pan. Let the cake continue cooling on the cooling rack until completely cooled.

In a small bowl mix the pistachio milk, sweetened condensed milk, lemon zest and vanilla together.

Let the mixture sit for 20 minutes. Then, pass it through a sieve to remove the zest, transferring it to a liquid measuring cup.

Add the pistachios to a food processor and pulse until very finely ground into a smooth paste.

Add the butter to a large mixing bowl and mix on high speed with an electric mixer until pale and fluffy, about 5 minutes.

Then add in the cream cheese and mix on high speed until fluffy, about 1 minute.

Add in the ground pistachio paste and lemon zest. Mix on medium high until combined.

Sift in the powdered sugar. Mix on low speed until combined, then on high speed for 1 minute until fluffy again.

When the cake is completely cooled, cut a very thin layer off the top of the cake using a sharp knife.

Poke holes on the top of the cake using a wooden stick or the handle of a wooden spoon.

Slowly pour the pistachio milk mixture on top of the cake.

Frost the top of the cake with a thick layer of lemon pistachio cream cheese frosting.

Swirl lemon curd into the frosting.

Then cut into 16 slices and serve!