Place eggs in the bowl of a stand mixer fitted with whisk attachment. Whisk on medium-high speed until frothy. With the motor running, gradually add sugar. Slowly pour in the melted butter, then whip.
Reduce the mixer speed to low, then carefully add ground pistachios, almond flour, lemon zest, almond extract, rose water, and baking powder. Continue mixing, then use a spatula to scrape the sides and bottom of the bowl. Mix once more.
Pour the mixture into the prepared cake pan – the batter will be fairly thin. Tap the cake pan on the counter twice to release any air bubbles, then bake until a cake tester inserted into the center of the cake comes out clean. Place the pan on a wire rack, then cool.
Combine powdered sugar, milk, and rose water in a small bowl, then whisk until smooth.
Pour the glaze over the cake, allowing it to drop over the sides. Sprinkle as many chopped pistachios and dried rose petals (if using) right on top as you like. Allow to set, then cut into slices. Enjoy!