Preheat the oven to 325° F. Grease a pound cake pan. With an electric mixer, cream the butter, oil, lemon zest and sugar on medium-high until light and fluffy, about 4 minutes. Add the eggs; mix for 1 additional minute at medium speed. Add the cake flour, finely ground pistachios, baking powder and salt to the mixture. Mix on low speed for about 20 seconds. Scrape the side and bottom of the bowl, and then mix for 1 additional minute at low-medium speed. Pour the batter into the greased pound cake pan and bake for 1 hour at 325° F, or until the cake is cracked on top and a toothpick inserted in the center of the cake comes out clean. Let the cake cool in the pan for 10 minutes; then remove it to a serving plate.

Make a syrup with the sugar and the water – cook for about 2 minutes after it starts to boil. Spoon the syrup over the pound cake; sprinkle the whole pistachios over the syrup. Let cool for 30 to 40 more minutes before slicing and serving.