Preheat oven to 350°F. Line 2 cookie sheets with parchment paper or silicone baking mats.
Whisk flour, salt, and baking soda in a medium bowl. Set aside.
Place ½ cup pistachios in a food processor and pulse until roughly chopped. Remove from food processor to a small bowl and set aside.
Place remaining 1 cup pistachios in the food processor. Run the processor until the pistachios become a smooth butter consistency. Every 30 seconds or so, stop the processor and scrape the bottom and sides. It will get dusty, then thick like paste, then eventually smooth like a natural nut butter.
Transfer the pistachio butter to a large bowl or the bowl of a stand mixer. Add butter and mix until combined, then add both sugars and cream until fluffy.
Mix in egg, vanilla, and almond extract until smooth, then add dry ingredients and mix until dough forms.
Add reserved chopped pistachios and chocolate chips.
Scoop 2 tablespoon size balls of cookie dough onto prepared cookie sheets, 2-inches apart. Press lightly with the palm of your hand so they’re not super rounded.
Bake until the tops are no longer glossy and the edges are light golden brown, about 10-14 minutes. Cool at least 10 minutes before removing from cookie sheets.
Store in an airtight container for up to 4 days or freeze cooled cookies for several months.