Preheat oven to 350°F (175°C). Grease and line a 9×13-inch baking pan.
In a food processor, blend all-purpose flour and ground pistachios until well incorporated.
Sift the flour-pistachio mixture into a large bowl. Add baking powder and salt. Whisk to combine.
In another bowl, use an electric mixer to cream unsalted butter with 1 ½ cups granulated sugar until light and fluffy.
Add eggs one at a time, mixing thoroughly after each. Stir in vanilla extract and 1 teaspoon rose water.
Gradually incorporate the dry ingredients into the wet, alternating with ¾ cup whole milk. Mix just until combined.
Pour the batter into the prepared pan. Spread evenly and sprinkle remaining ground pistachios on top.
Bake for 35 minutes or until the edges are golden and a toothpick inserted in the center comes out clean.
In a saucepan over medium heat, combine 2 cups whole milk, ½ cup granulated sugar, and 1 tablespoon rose water. Stir until sugar dissolves, then let cool.
After the cake cools, cut into 12 squares. Drizzle a small amount of cooled rose syrup over each serving as you plate.
Chill the assembled cake in the refrigerator for at least 4 hours, ideally overnight, to absorb the syrup.