Heat the oven to 350ºF. Line a cookie sheet with parchment or a silpat.
In a food processor, grind the nuts for about 45 seconds, or until the form a fine meal. With the motor still running, drizzle in the olive oil to form a paste resembling crunchy peanut butter.
In a mixing bowl, beat the pistachio butter and butter until smooth. Beat in the sugars until light and fluffy. Mix in the egg and vanilla.
In a second bowl, combine the flour, baking soda, baking powder, and cardamom. Stir the dry ingredients into the wet ingredients until a soft dough forms.
Drop teaspoon-sized balls of dough onto the prepared baking sheet, about 2 inches apart. Bake 15-18 minutes or until the edges are golden brown (the centers will still be pale and soft, but will collapse and darken slightly as the cookies cool.)