Step 1: Preheat your oven to 350°F (175°C). Grease and flour a 9-inch round springform pan. You can also line the bottom with parchment paper for easier release.
Step 2: In a medium bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt. Set aside.
Step 3: In a large mixing bowl, whisk together the granulated sugar and lemon zest until fragrant. Add the eggs, one at a time, whisking well after each addition until the mixture is light and fluffy. Continue whisking in the extra virgin olive oil and fresh lemon juice until fully combined and smooth.
Step 4: Gradually add the dry ingredient mixture to the wet ingredients, mixing on low speed or by hand with a spatula until just combined. Be careful not to overmix; a few streaks of flour are acceptable.
Step 5: Gently fold in the chopped Medjool dates and chopped pistachios until evenly distributed throughout the batter. Reserve a small amount of pistachios for garnishing if desired.
Step 6: Pour the batter evenly into your prepared springform pan. Sprinkle with reserved pistachios if using. Bake for 40-50 minutes, or until a wooden skewer inserted into the center comes out clean and the top is golden brown.
Step 7: Once baked, remove the cake from the oven and let it cool in the pan on a wire rack for about 15-20 minutes. Carefully release the springform sides and transfer the Date Pistachio Lemon Olive Oil Cake to the wire rack to cool completely before slicing and serving.