Begin by preheating your oven to 350°F (175°C). While the oven heats, line a baking sheet with parchment paper to prevent sticking.
In a large mixing bowl, use an electric mixer to beat the softened butter until it becomes creamy and smooth, about 2-3 minutes.
Gradually add the sifted powdered sugar and granulated sugar to the butter, continuing to mix until the mixture is well combined and fluffy in texture, roughly 2-3 additional minutes.
Incorporate the large egg, rose water, and vanilla extract into the butter and sugar mixture. Mix until all ingredients are fully blended and smooth.
In a separate bowl, whisk together the all-purpose flour, baking powder, and salt to combine the dry ingredients. Slowly add this dry mix to the butter mixture, stirring gently until a soft and slightly sticky dough forms.
Carefully fold in the finely chopped pistachios, ensuring they are evenly distributed throughout the cookie dough for delightful bites in every cookie.
Using a tablespoon, scoop out portions of dough and roll them into small balls. Place the dough balls on the lined baking sheet, ensuring they are spaced about 2 inches apart to allow for spreading during baking.
With the palm of your hand, lightly press each cookie ball down to flatten slightly. Sprinkle a few extra chopped pistachios on top of each flattened cookie for added texture and visual appeal.
Place the baking sheet in the preheated oven and bake for 10-12 minutes, or until the edges are just lightly golden. Keep an eye on them to avoid overbaking.
Once baked, remove the cookies from the oven and let them cool on the baking sheet for about 5 minutes. Afterward, carefully transfer them to a wire rack to cool completely, allowing airflow to maintain their texture.
Notes
For an elegant serving suggestion, stack the cookies on a tiered dessert stand or arrange them neatly on a decorative plate.