Preheat your oven to 350*F (175*C).
Grease the bottom and sides of 9-inch round cake pan or springform pan with some butter and line the bottom with parchment paper and set aside.
In a food processor or blender, pulse 1 cup shelled unsalted pistachios, and 1/2 tsp cardamom powder till it forms a fine powder.
Place the ground pistachio mixture in a large bowl, add 1 cup almond flour, 1 cup semolina, 1 1/4 tsp baking powder and 1/4 tsp salt. Mix well and set aside.
In an electric mixer with whisk attachment, cream the 1 cup butter and 3/4 cup sugar till light and fluffy (about 5 mins). Scrape down the sides of the mixer, and cream the butter one more time to make sure it is well blended. Slowly add the 4 eggs, one at a time, mixing well to combine, and scraping down the sides, before adding each one.
Remove the wet ingredients from the electric mixer. Now, using a spatula, gently start to fold the wet ingredients into the dry ingredients. Be careful not to over mix.
Add the 1 tsp lemon zest, 1 tbsp lemon juice, 2 tbsp rose water and 1/2 tsp vanilla extract and fold it a few more times till just mixed. Again, be careful not to over mix. The batter will be quite thick.
Pour the batter into the prepared baking dish (it will be quite thick) and spread out with the back of your spatula to fill the pan. Bake for 55 to 60 mins till the edges turn golden, top is firm, and a wooden toothpick inserted into the centre of the cake comes out clean, but oily.
Let the cake rest for at least 10 mins before removing from the pan. Allow to cool completely before glazing and serving.