Scoop eight 1-tablespoon portions of pistachio cream onto a parchment-lined tray and freeze until firm.
Brown the butter in a small saucepan over medium heat until amber with toasted brown specks, then cool in the freezer for 5 minutes.
Whisk both sugars into the cooled brown butter, followed by the egg and vanilla.
Fold in the flour, baking powder, baking soda, and salt just until a few flour streaks remain.
Fold in the chopped chocolate and crushed pistachios until the flour disappears.
Divide the dough into eight heaping portions, flatten each, enclose one frozen pistachio-cream portion, and roll closed.
Cover and chill the dough balls for 30 minutes while heating the oven to 350°F.
Space the dough balls on a parchment-lined baking sheet, spoon a little extra pistachio cream on top, and bake for 12 to 14 minutes until the edges are lightly golden.
Cool on the hot tray for 5 minutes before transferring the cookies to a rack.