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To make the cake: Preheat the oven to 425°F. Spread the pistachios on a baking sheet and toast until fragrant and browned, about 5 minutes. Allow the pistachios to cool, then pulse in a food processor until finely ground. Set aside.
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Reduce the oven temperature to 350°F.
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In a medium bowl, whisk together the flour, baking powder, cardamom, and salt; set aside.
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Using a stand mixer fitted with the paddle attachment (or electric beater), beat the butter and sugar together until light and airy. Add the eggs one at a time and beat to incorporate, scraping the bowl as needed. Mix in the vanilla extract and rose water.
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Alternate adding the flour mixture and milk, starting and ending with the flour. Mix until the dry ingredients are just incorporated between each addition, scraping the bowl as needed.
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Grease a small (5- to 6-cup) Bundt pan or 8 1/2" x 4 1/2" loaf pan.
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Fold the pistachios into the batter, then scoop the batter into the prepared pan.
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Bake the cake for 30 to 35 minutes in the Bundt pan, or 40 to 50 minutes in the loaf pan (tenting with aluminum foil after 40 minutes to prevent over-browning). A toothpick inserted into the center should come out clean.
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Remove the cake from the oven and let it cool for 10 minutes, then invert it onto a cooling rack to cool completely.
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To make the icing: Sift the confectioners’ sugar and cardamom into a medium bowl, then whisk in the lemon juice and cream.
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Drizzle the icing over the completely cooled cake.
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Garnish with the chopped pistachios and dust with gold luster dust, if desired.
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Store leftover cake, covered, at room temperature for several days. Freeze un-iced cake, well wrapped, for longer storage.