Preheat the oven to 350 degrees. Line the bottom of a 9-inch springform pan with parchment paper and spray the sides with baking spray.
In a large bowl, combine the flour, ground pistachios, baking powder, baking soda, salt and sugar.
In a medium bowl, whisk together the eggs, lemon juice, lemon zest, buttermilk, olive oil and vanilla until combined.
Pour the wet ingredients into the dry ingredients and stir together until just combined without over mixing.
Pour the batter into the prepared pan. Bake for 45-50 minutes, until a cake tester or toothpick comes out with moist crumbs.
Let the cake cool in the pan. Once cooled, run a sharp knife around the edges and then remove the ring of the springform pan. Either top the cake with the whipped cream or serve it on the side. Top with more lemon zest and pistachios if desired.