Step 1: Preheat your oven to 350°F (175°C) and grease a 9×5-inch loaf pan or line it with parchment paper. Set aside.
Step 2: In a medium bowl, whisk together the all-purpose flour, finely ground pistachios, baking powder, baking soda, salt, and ground cardamom.
Step 3: In a large mixing bowl, beat the softened unsalted butter and granulated sugar together until the mixture is light and fluffy, which should take about 3-4 minutes.
Step 4: Add the eggs one at a time, ensuring each is fully incorporated before adding the next. Stir in the lemon zest, fresh lemon juice, and vanilla extract until well combined.
Step 5: Gradually add the dry ingredient mixture from Step 2 to the wet ingredients. Mix until just combined, being careful not to overmix the batter.
Step 6: Pour the prepared batter evenly into the greased or lined loaf pan. Smooth the top with a spatula. Bake in the preheated oven for 50-60 minutes, or until a toothpick inserted into the center of the cake comes out clean.
Step 7: Remove the loaf from the oven and allow it to cool in the pan for about 10 minutes. After 10 minutes, carefully transfer the cake to a wire rack to cool completely.
Step 8: While the cake cools, prepare the lemon glaze: In a small bowl, whisk together the powdered sugar and 2-3 tablespoons of fresh lemon juice until you achieve a smooth, pourable consistency. Adjust lemon juice as needed.
Step 9: Once the loaf cake has cooled completely, drizzle the prepared lemon glaze evenly over the top, allowing it to artfully drip down the sides of the cake.
Step 10: Slice the loaf cake and serve immediately. Enjoy this delightful treat with your favorite hot beverage!