Step 1

For the Cake: Preheat oven to 325°F with a rack in center. Brush the hollows of a mini Bundt pan with butter. Dust with flour, tapping out excess. Whisk together egg and yolk, milk, nut extract, and orange‐flower water.

Step 2

Pulse pistachios in a food processor until finely ground. Add confectioners' sugar; pulse to combine. Transfer mixture to the bowl of a mixer fitted with the paddle attachment and add flour, baking powder, and salt. Beat on low speed to combine.

Step 3

Continue beating while gradually adding butter until mixture is crumbly, 1 to 2 minutes. Slowly add half of milk mixture; increase speed to medium and beat until light and fluffy, 1 to 2 minutes. Slowly add remaining milk mixture and beat, scraping down bowl as needed, until incorporated, about 15 seconds.

Step 4

Divide batter evenly among hollows of prepared pan (using a piping bag fitted with a coupler or a plain large tip makes neat work of this). Bake until tops are light golden and spring back when lightly touched, about 30 minutes.

Step 5

Let cool in pan on a wire rack 10 minutes, then turn out onto rack and let cool completely, about 30 minutes. (Cakes can be stored unglazed, wrapped in plastic, at room temperature up to 2 days.)

Step 6

For the Glaze: Whisk milk into sugar until mixture has the consistency of thick white glue. Stir in orange‐flower water. Glaze can be stored in an airtight container at room temperature up to 1 week.

Step 7

Spoon glaze over tops of cakes, allowing it to drip down sides. Sprinkle with chopped pistachios and rose petals; let stand until set, about 30 minutes.