Preheat oven to 350°F (175°C). Line a baking sheet with parchment paper.
Grind the pistachios in a food processor with 1 tablespoon of the powdered sugar (taken from the 1 cup). Pulse until finely ground, being careful not to overprocess.
Transfer the ground pistachios to a medium mixing bowl. Add the remaining powdered sugar, almond flour, and salt. Stir to combine.
Add the egg whites, vanilla extract, and almond extract. Mix with a spatula until a thick, sticky dough forms.
If the dough is too sticky, refrigerate for 15 minutes. This makes it easier to form the cookies, and it helps keep their round shape and prevents them from flattening while baking.
Scoop about 1 tablespoon of dough and roll. If you have it, use a 1-tablespoon size cookie scoop - no need to shape - Drop directly into a plate of powdered sugar. Roll to coat well.
Place cookies on the prepared baking sheet, spacing them slightly apart.
Bake for 11–12 minutes, until the tops crack slightly and the bottoms are just lightly golden at the edges. The cookies should remain soft and pale.
Let cookies cool completely on the baking sheet to set the chewy centers.
