Preheat the oven to 350°F. Brush a Bundt pan generously with olive oil.
Grind ¾ cup of pistachios in a food processor until finely ground; be careful not to over process and turn into paste. Measure ¾ cup of the ground pistachios and save the rest, if any, to garnish. Coarsely chop the remaining 2 tablespoons of pistachios and set aside.
In a large mixing bowl, whisk together the ¾ cup ground pistachios, olive oil, sugar, eggs, milk, vanilla, and lemon zest until well combined and fluffy, about 1 minute. In another bowl, whisk together the flour and baking powder. Stir the flour mixture into the wet ingredients and mix thoroughly. Bake for 40-50 minutes or until a toothpick inserted into the center comes out clean. Place the pan on a cooling rack and let cool for 10 minutes. Invert the cake onto the cooling rack and let cool completely.
Whisk together the powdered sugar with lemon juice, 1 tablespoon at a time. You want a mixture that is a thick, pourable glaze.
Put waxed paper or parchment paper under the wire cooling rack and drizzle the glaze over the top of the cake, letting it drip down the sides and in the middle hole. Top with the chopped pistachios and any finely ground pistachios you have left over, if any. Let the icing set, then transfer to a cake plate or stand.
This cake is very moist and can be made two days ahead. Store, covered, at room temperature or in the refrigerator. If stored in the refrigerator, let come to room temperature before serving.