In a heatproof bowl, melt the butter. Add the sugar, salt and vanilla and whisk well to combine, 3-5 minutes until you cannot see any butter separated. Pour in the tahini and whisk just a bit. Now add the egg and whisk well.
Sprinkle in the flour, salt, powder and soda and use a rubber spatula to mix the dough. Crumble the halva over the dough and stir to combine, stir in the chocolate. Cover with plastic wrap and set in the fridge for two hours or overnight.
Preheat the oven to 350 F. Line two greased cookie sheets with parchment paper.
Scoop the dough onto the pan, about 1 ½ tablespoons per cookie, or 3 tablespoons dough per cookie if you want large ones; but leave about 1 inch between as they will spread. Press in some extra chocolate on top.
Bake for 10-12 minutes until the edges are golden for smaller cookies and up to 15 minutes for bigger cookies.