Preheat oven to 350 degrees F.
Once you have all your ingredients gathered, add the butter and sugar to a large mixing bowl. Then, cream the butter and sugar together, using a handheld electric mixer. By the way, I used cold butter and not room temperature butter.
After that, add the eggs in one by one and mix well.
Add the pistachios to a small food processor or high-powered blender and blend them until they are a flour-like consistency. Then, add these ground up pistachios to the large bowl.
Then add in the vanilla extract, almond extracts, baking powder, cardamom, semolina flour, and ginger, the bowl and mix well.
Using a microplane grater, grate the zest off the whole lemon into the bowl with the pistachio cake batter, which measured about 1.5 teaspoons of lemon zest.
Cut the lemon in half and juice it, while measuring out 1.25 tablespoons of the lemon juice. Add the lemon juice to the batter as well and mix well so all ingredients are well incorporated. Do not discard the rest of the lemon juice as we will use it to make a lemon syrup to brush over the warm cake as well as a lemon icing.
The pistachio cake batter will be very thick. Set it aside and line a loaf pan with parchment paper and sprayed with nonstick spray.
Using a spatula or spoon, spoon the batter into the parchment-lined loaf pan.
Bake the pistachio cake for 35-40 minutes in an oven that has been preheated to 350 degrees. Text to see if the cake is baked by inserting a toothpick into its center. If the toothpick comes out clear, then the cake is ready to be cooled. However, if the toothpick has batter on it, bake it for 5 more minutes and repeat the test.
While the cake is baking, mix together 1 tablespoon of lemon juice with 1 tablespoon of granulated sugar and set it aside.
When the cake is baked through, remove it from the oven and brush the lemon juice/sugar mixture over it while it is still warm. Then let the cake cool on a wire rack and plate it on a serving dish.