Preheat your oven to 350°F (175°C) and prepare a 9x9 inch baking pan.

In a food processor, pulse the deshelled pistachios until finely ground.

Whisk together flour, baking powder, baking soda, and salt in a bowl.

Rub lemon zest into sugar, then add softened butter and cream together until fluffy.

Mix in eggs and vanilla extract until smooth.

Gradually add buttermilk and dry ingredients, mixing until combined.

Fold in ground pistachios gently to maintain airiness.

Pour batter into prepared pan and bake for 38-42 minutes until golden.

Cool the cake in the pan for 30 minutes, then finish cooling on a wire rack.

Combine pistachio milk, sweetened condensed milk, lemon zest, and vanilla; let sit for 20 minutes before straining.

Beat softened butter until fluffy, mix in cream cheese, then add pistachio paste and powdered sugar until creamy.

Trim the top, poke holes in cake, pour milk soak over, and frost generously before serving.