Measure your flour into a bowl and whisk to aerate the flour and remove any lumps.
In a large mixing bowl of the bowl of a stand mixer combine the butter, brown sugar, salt, almond extract and vanilla extract. Mix on low until ingredients are roughly combined then increase mixer speed to medium and beat until mixture is lighter in color and fluffy, about 2 minutes.
Add the flour all at once and mix on low speed until the flour is well combined and the dough has started to come together about 3 minutes. The cookie dough will have a crumbly texture in the beginning and then it will come together into a smooth dough. Add the chopped pistachios and dried apricots and mix on low speed until well combined, about 30 seconds.
Turn the cookie dough out onto a lightly floured surface. You can turn it out onto a large piece of parchment paper or Silpat. Use your hands to shape the dough into a large ball and then divide it in half. Each half should weigh about 350 grams. Shape each half into a log about 6 inches long and 2 inches thick. Wrap each log in plastic wrap and refrigerate for at least 2 hours.
Preheat the oven to 300 degrees F. Line a cookie sheet with parchment paper or Silpat.
Using a sharp knife to slice the ends of the cookie logs to even out the ends. Slice each log into 1/4-inch rounds and place each slice on a cookie sheet about 1-inch apart. These cookies don’t spread much. Bake for 22-25 minutes. Remove the cookies and allow to cool.
Store the cookies in an airtight container.