Preheat the oven to 350°F (180°C). Grease and flour a 9-inch round cake pan.
In a mixing bowl, cream the butter and powdered sugar until light and fluffy.
Add lemon zest and vanilla extract, mix well.
In a separate bowl, combine the flour, ground pistachios, baking powder, and salt.
Gradually add the dry ingredients to the butter mixture, alternating with the milk.
Beat in the eggs one at a time until well combined.
Gently fold in the fresh raspberries.
Pour the batter into the prepared cake pan and smooth the top.
Bake for 30-35 minutes or until a toothpick inserted into the center comes out clean.
Allow the cake to cool in the pan for 10 minutes before transferring to a wire rack to cool completely.