Heat the oven to 350 degrees F.
Cut a piece of parchment paper. Fit it into the bottom of a 9-inch by 5-inch by 2 ½-inch loaf pan. Secure it to the bottom of the pan with a few dabs of vegetable shortening.
Grease the pan well with vegetable shortening (including the surface of the parchment bottom). Sprinkle flour into the pan and shake out the excess.
In a mixing bowl, whisk together 1 ½ cups all-purpose flour, ¼ teaspoon baking powder, ¼ teaspoon baking soda, ¼ teaspoon salt, and 1 to 2 teaspoons ground cardamom. Set aside.
Whip 8 tablespoons unsalted butter and 1 cup granulated sugar until light and fluffy (about 2 minutes).
Add the 2 large eggs and continue to whip until well incorporated and smooth.
Whip in the lemon zest, then set aside for a moment.
In a separate bowl or liquid measuring cup, whisk lemon juice, yogurt, milk, and vanilla extract together. Set aside.
Whip the dry and wet ingredients into the butter mix, little by little, alternating between the two. Whip for a few minutes on high speed until you have a very smooth and creamy-looking batter.
Fill the batter into the loaf pan. Bake until a toothpick inserted into the center of the cake comes out completely clean (45 to 60 minutes). Check in several spots along the center length of the cake to make sure that the cake is fully baked.
Once the pan is cool enough to handle, run a knife around the edges to loosen the cake from the sides of the pan. Unmold the cake and let it cool completely.
Whisk powdered sugar and lemon juice together. Keep adding lemon juice until you have a slow-moving icing. If the icing ends up too runny, whisk in a little more powdered sugar.
Drizzle the icing on the cake and sprinkle the chopped pistachios on.
