Mix the flour, salt, baking soda, and baking powder in a medium bowl until well combined. Set aside.
In a large bowl, use a hand mixer or stand mixer to beat together the olive oil, butter, and both sugars until smooth. You do not need to cream until light and fluffy, but the mixture shouldn’t have large lumps of butter.
Add the zest, vanilla, and egg, and beat until well combined.
Add the flour mixture and beat until just combined. Fold in the chopped pistachios by hand.
Cover the dough and refrigerate for at least 1 hour.
Preheat oven to 350°F. Line two baking sheets with parchment paper.
Scoop tablespoon-sized balls of dough onto the cookie sheets, then press lightly to flatten the top of each ball. Bake for 9-11 minutes, or until the edges of the cookies are lightly browned. They will be fairly pale.
Cool the cookies on the pan for 10 minutes before transferring to a wire rack to cool completely.
For the icing, combine the powdered sugar, vanilla, and 1 tablespoon of hot water in a small bowl. Add additional water in ½ teaspoon increments until the icing is easy to drizzle.
Drizzle each cookie with icing and sprinkle with roasted pistachios. Allow to dry before storing for up to 1 week in an airtight container.
Servings 30