Preheat the oven to 350°F. Generously grease a 16x12-inch sheet pan, then line it with greased parchment paper.

In a stand mixer fitted with the whisk attachment, combine the egg whites, salt, and cream of tartar and beat on medium-high speed until medium peaks form, about 3 minutes.

Turn the mixer speed to medium-low and drizzle in the water. Slowly sprinkle in the sugar a little at a time; this may take a minute or so. Turn the speed to high and whip until very stiff, glossy peaks form, about 5 minutes.

Using a rubber spatula, gently fold the cornstarch, vanilla, and vinegar into the egg whites.

Evenly spread the pavlova batter in the prepared pan. Bake until the pavlova starts to turn a light caramel color, about 20 minutes. It will puff considerably while it bakes but will settle once it is out of the oven. Let the pavlova cool completely. (Just leave it in the pan, dust with confectioners’ sugar, and cover with a clean kitchen towel for up to 1 day.)

Heat the heavy cream to a simmer. Turn off the heat and add the chopped chocolate.

Swirl the pan to submerge the chocolate. Let sit for 3 minutes then gently whisk until smooth. Keep in pot until ready to use.

In the bowl of a stand mixer fitted with the paddle attachment, beat confectioners’ sugar, butter, salt, and vanilla at medium speed until smooth.

Add enough tahini, while beating, to make a smooth, spreadable frosting. Beat until combined and smooth, stopping to scrape sides of bowl. Use immediately.

Loosen the pavlova from the pan. Spread 1 cup of the ganache over the pavlova and sprinkle with the crushed halva and all but 2 tablespoons of the pistachios. Refrigerate until solid.

Spread the buttercream over the chilled ganache. Refrigerate until solid.

Cover the cake with plastic and invert onto the back of a second baking sheet. Remove the parchment from the bottom and invert onto a cutting board. Cut the cake in half along the long side and in thirds on the short side, so you have 6 sections. Stack the sections. Use a knife dipped in hot water to clean up any straggly bits.

Pour the remaining ganache over the top of the cake and sprinkle with remaining pistachios. Transfer to serving plate. Serve at room temperature.