Preheat your oven to 350°F (175°C) and grease a 9-inch round cake pan with butter or non-stick spray, lining the bottom with parchment paper.

Place the shelled pistachios in a food processor and pulse until finely ground into a flour-like texture, being careful not to over-process into a paste.

In a medium bowl, whisk together the ground pistachios, all-purpose flour, baking powder, and salt until well combined.

In a large mixing bowl, cream the softened butter and granulated sugar together using an electric mixer on medium speed until light and fluffy, about 3-4 minutes.

Add the eggs one at a time, beating well after each addition, then mix in the vanilla extract and lemon zest.

Gradually add the dry ingredient mixture to the wet ingredients, alternating with the milk, starting and ending with the dry ingredients.

Mix on low speed until just combined, ensuring you do not overmix the batter to keep the cake tender.

Pour the thick batter into the prepared cake pan and smooth the top evenly with a spatula.

Bake in the preheated oven for 40-45 minutes, or until a toothpick inserted into the center comes out clean and the top is golden brown.

Remove the cake from the oven and let it cool in the pan for 10 minutes before transferring it to a wire rack to cool completely.

Once the cake is fully cooled, dust generously with powdered sugar before slicing and serving.