Heat the egg whites and sugar.
Bring a little water to a gentle simmer in a saucepan. Place a heatproof mixing bowl over the pan, making sure the bottom does not touch the water.
Add the egg whites and sugar. Whisk constantly until the sugar dissolves and the mixture reaches 160°F on an instant-read thermometer. This may take about 5–7 minutes, but use the temperature as your guide.
The mixture should feel smooth with no sugar grains; checking the texture alone does not confirm the temperature.
Whip the meringue.
Carefully remove the bowl from the heat. Using a stand mixer fitted with a whisk attachment or a hand mixer, beat for about 4 minutes.
Add the vanilla and beat for another 2 minutes. Add the vinegar and salt, then continue whipping until the meringue forms stiff, glossy peaks and the bowl no longer feels warm.
Pipe onto the biscuits.
Arrange the biscuits on a parchment-lined tray.
Transfer the meringue to a piping bag fitted with a large round tip, or a sturdy zip-top bag with a corner snipped off. Pipe a tall mound onto each biscuit, leaving a narrow edge around the base.
Refrigerate until thoroughly chilled, or freeze briefly until firm enough to dip. The meringue will remain soft inside.
Prepare the chocolate coating.
Place the chocolate in a microwave-safe bowl. Microwave in 30-second intervals, stirring between each, until melted and smooth.
Stir in the coconut oil. Let the chocolate cool until barely warm but still fluid.
Dip the Tarboosh.
Holding each biscuit by its edges, carefully dip the meringue into the chocolate, coating the top and sides. Lift gently and let excess chocolate drip off.
If dipping feels difficult, hold the cookie over the bowl and spoon chocolate over the meringue instead.
Return to the lined tray.
Chill and serve.
Refrigerate for about 1 hour, until the chocolate coating is firm. Serve chilled.