Pour 1-2" water into a small to medium sized pot. Heat water over medium high heat. Once the water starts to come to a simmer, place the bowl with the chocolate chips, tahini and butter on top of the pot with simmering water (double boiler).
Fully melt the ingredients, stirring to combine. Whisk until all the chocolate has melted and the tahini and butter has been fully mixed in. Remove from heat and set aside.
Pour 1/2 of the tahini ice cream base into the freezer proof container. Drizzle 1/2 of the tahini ganache and crumble 1/2 of the halva on top. Repeat a second layer.