Heat the oven to 350°F and line a 9-inch square ceramic baking dish with parchment paper, leaving two sides hanging over the edge for lifting later.
Melt 1 cup unsalted butter and 8 ounces chopped bittersweet chocolate together in a small saucepan over low heat, stirring often, until completely smooth, about 4 minutes.
Pour the warm chocolate mixture into a large mixing bowl and whisk in 1 1/2 cups granulated sugar and 1/2 cup brown sugar until the batter looks glossy.
Whisk in 4 eggs one at a time, then 1 tablespoon vanilla extract, beating until the batter turns a shade lighter and falls off the whisk in a slow ribbon.
Sift 3/4 cup cocoa powder, 1 cup flour, and 1/2 teaspoon salt over the batter and fold with a wooden spoon just until no dry streaks remain; stop as soon as it is smooth so the brownies stay fudgy, not cakey.
Pour the batter into the prepared baking dish, smooth the top, and bake for 26 to 30 minutes, until the edges look set and a toothpick inserted in the center comes out with a few moist crumbs attached.
Set the dish on a wire rack and let the brownies cool completely, about 1 hour at room temperature, before adding anything on top.
While the brownies cool, toast 6 ounces chopped kataifi in a medium skillet with 4 tablespoons melted butter and a pinch of salt over medium heat, stirring constantly, until the strands turn deep golden brown and smell toasted, 6 to 8 minutes.
Stir the toasted kataifi into 1 1/4 cups pistachio cream, 2 tablespoons tahini, and 1/4 teaspoon salt in a white mixing bowl, folding until every strand is coated and the mixture is evenly green (add a small drop of green food coloring here if you want a brighter stripe).
Spread the pistachio mixture over the cooled brownies in an even layer, pressing gently with the back of a spoon into the corners, then refrigerate for 30 minutes, until firm to the touch.
Melt 10 ounces chopped chocolate with 1 tablespoon oil in a clean bowl set over barely simmering water, stirring until glossy, then pour it over the chilled pistachio layer and tilt the dish so it reaches every edge.
Return the dish to the refrigerator and chill for 20 to 30 minutes, until the chocolate shell is firm enough that it sounds hollow when tapped.
Lift the whole slab out using the parchment overhang, set it on a wooden board, and cut into 16 squares with a large sharp knife, wiping the blade clean between cuts so each square shows a crisp green stripe.