In a food processor, pulse pistachios until small crumbs form. 6 oz. very finely chopped nuts are needed.
Combine the confectioners' sugar, vanilla extract, and almond extract in a medium-high-powered mixer and beat until smooth.
Refrigerate the cookie dough for 30 minutes or up to 3 days if covered tightly (See note)
Preheat the oven to 350°F and prepare large baking sheets with parchment paper or silicone baking mats.
Roll the cookie dough into 1-tablespoon balls and space them 2 inches apart on the baking sheets.
Continue rolling and working the dough with your hands if it becomes too crumbly. Your hands' warmth will aid in bringing it all together.
Bake the cookies for 15 minutes, or until lightly browned on top and bottom, for medium-rare cookies.
While the cookies cool, melt the chocolate in a double boiler or use a bowl over a pan of water.
Make sure cookies are cool to the touch before dipping them in icing, or they will stick to the bottoms of the pans.
Dip half of each cookie in the icing and set onto the parchment to harden. The chocolate should harden within a few minutes.
Cover leftover iced cookies tightly with plastic wrap and store at room temperature for 1 day or in the refrigerator for up to 1 week.