Preheat the oven to 325°F. Spray a 1-pound loaf pan (8 x 4 inches) with nonstick spray and line it with parchment paper.

In a small bowl, whisk together the all-purpose flour, baking powder, and salt. Set aside.

Add the lemon zest to the sugar and rub it between your fingers to release the lemon oils into the sugar.

In the bowl of a stand mixer, beat the butter, olive oil, and lemon sugar on medium speed for about 5 minutes until light and fluffy. Scrape down the sides of the bowl.

Add the vanilla extract, then mix in the eggs one at a time, beating for 30–60 seconds between each addition. Scrape down the bowl as needed.

Mix in the lemon juice until incorporated.

Reduce the mixer to low speed and add half of the dry ingredients, followed by half of the Greek yogurt. Repeat with the remaining dry ingredients and yogurt, mixing just until combined.

Remove the bowl from the mixer and gently fold in ½ cup of the chopped pistachios using a rubber spatula.

Spread the batter evenly into the prepared loaf pan.

Bake for 75–85 minutes, until the top springs back when lightly pressed and the internal temperature reaches about 200°F. Let the cake cool in the pan for 15 minutes, then remove and transfer to a wire rack to cool completely.

Whisk together the powdered sugar and lemon juice to form a thick icing.

Spread the icing over the top of the cake, letting it naturally drip down the sides.

Sprinkle the remaining chopped pistachios over the icing. Allow the icing to set for at least 30 minutes before slicing and serving.