Prep the pistachios: Place the pistachios in the bowl of a food processor and pulse several times until chopped but not yet finely ground. Scoop out and set aside 2 to 3 tablespoons of the chopped nuts (we’ll use those later for the cookie tops). Continue pulsing the pistachios in long pulses until finely ground, about 1 minute.

Brown the butter: Cut 10 tablespoons of butter into cubes. Place in a medium saucepan over medium heat and cook, stirring every few minutes or so, until the butter has browned, turning very foamy and nutty but not burnt, 5 to 8 minutes. Quickly add the finely ground pistachios to the butter and stir constantly until they smell very nutty and toasted, 2 to 3 minutes more. The nuts absorb some of the browned butter and darken in color. The mixture will be fragrant and thick and should be deeply speckled with brown. Using a rubber spatula, scrape the brown butter mixture into a large bowl. Add 1 ice cube to the butter and let the ice cube melt and the butter cool for 10 minutes (it will foam up again momentarily).

Make the cookie dough: Chop the dark chocolate into irregular ¼-inch to ½-inch chunks and set aside. To the cooled butter, add the brown sugar, granulated sugar, egg and vanilla extract. Whisk vigorously until well combined and thickened, about 1 minute. Add the all-purpose flour, kosher salt and baking soda, and stir well with a spatula or wooden spoon until combined into a sticky dough. Add half of the chopped chocolate along with the halva, pinching it lightly with your fingers as you add it to help it combine. Cover the top of the dough with plastic wrap and refrigerate for at least 3 hours and up to 2 days. (The longer you chill the dough, the more complex the flavor of the cookies will be, so, if you can, chill it overnight.)

Heat the oven to 375 degrees. Line two baking sheets with parchment paper. Using a 2-ounce ice cream scoop (or large spoon), scoop out 12 equal scoops of dough, about ¼ cup each. Working one at a time, dip the tops of the dough balls into the reserved chopped pistachios, then press into the remaining chocolate chunks and halva pieces (you want about 20% flair on top). Dot the tops of each cookie with a few more chopped nuts if you like. Place the dough balls on the prepared baking sheets, pressing slightly to flatten. Bake, rotating the sheets halfway through, until the cookies are golden brown at the edges but still soft in the middle, 10 to 12 minutes. While still warm, sprinkle the cookies with flaky sea salt. Once cool enough to handle, transfer to a wire rack to continue cooling. Store the cookies in an airtight container to make them last longer.