Preheat oven to 350°F. Liberally grease a large bundt pan with olive oil and set aside.
In a large bowl, whisk the olive oil, sugar, and eggs until fluffy, about 1 minute. Mix in the ground pistachios, milk, vanilla extract, and lemon zest.
In a separate bowl, mix together the flour, baking powder, and salt. Gently fold the mixture into the wet ingredients until combined. Pour into prepared bundt pan.
Bake for 40-50 minutes, until a knife inserted in the center of the cake comes out clean. Cool for 10 minutes before inverting onto a cooling rack.
To make the icing, whisk together powdered sugar and 2 tablespoons lemon juice. If the mixture is too thick, add in an additional tablespoon. Pour over cake and top with a sprinkling of chopped pistachios.
*to make ground pistachios, put a small amount of pistachios, about 1/4 cup at a time, into a high powered blender. You want to keep the amounts small so that it doesn't turn to paste-- it should stay dry. Repeat until you get 3/4 cup of finely ground pistachios.