• Preheat the oven to 350F. Grease and line the bottom of your 8" springform pan.
• Whisk together the 1 1/2 cups all-purpose flour, 1/3 cup finely ground pistachios, 1/2 tsp baking powder, 1/4 tsp baking soda, and 1/2 tsp fine sea salt. Set aside.
• Make the lemon sugar: place the 1 1/4 cups sugar and lemon peel into a food processor and process until the peel is completely incorporated and there are no chunks or pieces of peel left. The sugar will be pale yellow and fragrant. This will take under a minute, and you may want to pulse the machine at first to get the peel broken up.
• Transfer the lemon sugar to a mixing bowl (or a stand mixer) and cream the lemon sugar with softened 15 Tbsp unsalted butter until light and fluffy, about 3 minutes. Scrape down the sides of the bowl as needed.
• Beat in the 2 Tbsp vegetable or mild olive oil and the 3 large eggs, room temp, one at a time, allowing each egg to get incorporated before adding the next. Scrape the bowl.
• With your mixer on low, add the dry ingredients alternately with the 1/3 cup lemon juice ~ beginning and ending with the dry. Give the bowl a final sweep to make sure the sides and bottom are incorporated, and then turn the batter into your prepared pan. Smooth out the top.
• Bake the cake for 40-45 minutes, or until the center is set, the top springs back lightly, and a toothpick comes out without wet batter. My cake took 40 minutes.
• Let the cake cool in the pan on a rack for 10 minutes, then run an offset spatula around the edges to ensure they are loosened. Release the spring sides and allow the cake to cool completely before icing.

Make the icing

• Mix together the 1 1/2 cups powdered sugar and lemon juice until you have a thick glaze. Start with 3 Tbsp lemon juice, then add more as needed to make a thick but spreadable glaze. If there are small lumps, let the glaze sit for a few minutes and mix again.
• Spread the glaze over the top of the completely cooled cake. Dust with crushed pistachios. Let the glaze set up before slicing and serving.
• The cake is best the day it is made, but you can keep leftovers at room temperature loosely covered with foil or under a cake dome for up to 3 days. The cake will last for 5 days in the refrigerator.
• The cake can be frozen for up to 3 months, but I would add the glaze after thawing.