Preheat the Oven
Set your oven to 350°F (175°C) and grease a doughnut pan with butter or nonstick spray.
Mix Dry Ingredients
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.
Cream Butter and Sugar
In a large mixing bowl, use an electric mixer to cream the butter and sugar until light and fluffy.
Add Eggs and Vanilla
Beat in the eggs one at a time, ensuring each is fully incorporated. Stir in the vanilla extract.
Combine Wet and Dry Ingredients
Gradually mix the dry ingredients into the wet mixture, alternating with the milk, until just combined. Do not overmix! Gently fold in the chopped pistachios.
Fill the Doughnut Pan
Spoon or pipe the batter into the prepared pan, filling each cavity about two-thirds full.
Bake
Bake the doughnuts for 10-12 minutes, or until a toothpick inserted into the center comes out clean. Let them cool in the pan for a few minutes before transferring to a wire rack.
Prepare the Glaze
In a small bowl, whisk together powdered sugar, milk, and rose water until smooth. Adjust the consistency by adding more milk (for a thinner glaze) or powdered sugar (for a thicker glaze).
Glaze and Garnish
Dip the top of each cooled doughnut into the glaze, letting the excess drip off. Sprinkle immediately with crushed pistachios.
Let the Glaze Set
Allow the glaze to set for 10-15 minutes before serving.