Preheat the oven to 350?F. Spread the pistachios in an even layer on a rimmed baking sheet. Toast in the preheated oven for 10 minutes. Let cool slightly.

Brush a high-sided 8-inch round cake pan or springform pan with olive oil. Line the bottom of the pan with parchment paper and brush the parchment with a thin layer of olive oil and set aside.

Transfer the toasted pistachios to a food processor. Add 1 tablespoon of the sugar to the pistachios. Process until finely ground, about 1 to 2 minutes.

In a medium mixing bowl, whisk together the ground pistachios, flour, baking powder, baking soda, and salt.

In a large mixing bowl, whisk together the Greek yogurt, the remaining sugar, eggs, olive oil, and vanilla extract until thoroughly combined.

Add the flour mixture to the yogurt mixture and stir gently just until no streaks of dry flour remain.

Pour the batter into the prepared pan. Bake for 30 to 32 minutes, or until a toothpick inserted into the center of the cake comes out clean.

Let the cake cool in the pan for 15 minutes, then turn it out onto a wire rack to cool completely, about 1 hour.

In a small bowl, whisk together the pistachio butter, powdered sugar, and water until smooth. Add extra water, a teaspoon at a time, to thin to your preferred consistency.

When the cake has cooled completely, transfer it to a cake stand or serving plate. Pour the glaze on top of the cake and use an offset spatula or the back of a spoon to coax the glaze to the edges. Sprinkle the top with chopped pistachios. For clean slices, let the glaze set for at least 30 minutes before slicing and serving.