Preheat the oven to 350°F (175°C). Grease and flour a 9-inch round cake pan.
In a large mixing bowl, cream the butter and sugar until light and fluffy. Add the rosewater, vanilla extract, and eggs one at a time, mixing well after each addition.
In a separate bowl, whisk together the flour, baking powder, and salt. Gradually add the dry ingredients to the wet ingredients, alternating with the milk, until well combined.
Fold in the chopped pistachios.
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, then transfer it to a wire rack to cool completely.
Once cooled, you can optionally dust the cake with powdered sugar and decorate with additional pistachios.
Slice and serve the Pistachio Rosewater Cake.