Toast the kataifi and make the filling: Cut the kataifi into small pieces with kitchen scissors. Toss with melted butter and toast in a dry skillet over medium heat, stirring constantly, until deep golden brown, about 5-7 minutes. Let cool slightly, then stir it into the pistachio cream until fully combined.

Freeze the filling into portions: Scoop the filling into 1-tablespoon portions onto a parchment-lined tray. Freeze for at least 30 minutes, until firm enough to handle. This step is what keeps the filling from leaking out during baking, so don't skip it.

Make the cookie dough: Whisk melted butter, cocoa powder, and oil together in a large bowl. Let cool until no longer warm to the touch. Stir in both sugars, the egg, and vanilla until smooth.

Combine wet and dry ingredients: In a separate bowl, whisk together flour, baking soda, baking powder, and salt. Gradually add to the wet mixture, stirring just until a soft dough forms. Do not overmix.

Stuff the cookies: Scoop the dough into 2-tablespoon portions and roll into balls. Press your thumb into the center of each ball to form a well. Remove a frozen filling portion from the freezer and press it into the well, then fold the dough back around it to fully enclose the filling.

Bake: Place dough balls on a parchment-lined baking sheet, spacing at least 2 inches apart. Bake at 350°F (175°C) for 9-11 minutes, until the edges look set but the centers still look slightly underdone. Let cool on the baking sheet for 10 minutes before moving.

Finish: Once cooled, drizzle melted chocolate over each cookie and sprinkle with chopped pistachios. Let the chocolate set for about 10 minutes before serving.