Prepare the pan. Preheat an oven to 350°F (180°C). Line and grease a 9-inch round cake pan with parchment paper.
Combine the wet ingredients. Place 5 eggs (250g) in the bowl of a stand mixer fitted with whisk attachment. Whisk on medium-high speed until frothy, about 2-3 minutes. With the motor running, gradually add ½ cup (100g) sugar. Slowly pour in the melted butter, then whip an additional 1 minute until well mixed.
Add remaining ingredients. Reduce the mixer speed to low, then carefully add 1½ cup (180g) ground pistachios, ½ cup (65g) almond flour, 1 tsp lemon zest, 1 tsp almond extract, 2 tsp rose water, and ½ tsp baking powder. Continue mixing for about 1-2 minutes, then use a spatula to scrape the sides and bottom of the bowl. Mix once more.
Bake the cake. 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 for 25-30 minutes, or until a cake tester inserted into the center of the cake comes out clean. Place the pan on a wire rack, then cool for at least 1 hour.
Transfer to a cake stand. Invert the cake onto a cake stand or serving plate, then make the glaze.
Make the glaze. Combine ⅔ cup (80g) powdered sugar, 1 Tbsp milk, and 1 tsp rose water in a small bowl, then whisk until smooth. If the mixture is too dry, add up to 1 more tablespoon of milk.
Decorate the cake, then serve! 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 (for this, I like to sprinkle them around the outer perimeter of the cake only). Allow to set, then cut into slices. Enjoy!