Preheat the oven to 180°C/fan 160°C/gas mark 4. Grease and line three 18cm cake tins.
Add the oil, eggs, buttermilk and cauliflower to a free-standing mixer and beat until well combined. Combine the chocolate, sugar, flour, cocoa powder and baking powder, then add the liquid ingredients. Beat again until everything is well combined and you have a smooth batter. Divide the batter evenly between the three cake tins. Bake in the oven for 20-25 minutes until risen and firm to the touch. Leave to cool in the tins for 10 minutes, then turn out on to a wire rack to cool completely.
Meanwhile, beat the butter until soft. Add half the icing sugar and continue to beat until well combined. Add the remaining icing sugar and beat again. When the frosting is smooth, add the tahini and vanilla extract and beat again until well combined.
Level each cake so they are even. Place one of the cakes on a cake stand or board and spread with a quarter of the icing, making sure the icing goes all the way to the edges. Place the second cake on top and repeat. Finish with the final cake. Decorate the top with a swirl of icing, then use the remaining icing to skim the sides. Finish the cake with a ring of crumbled sesame snaps around the bottom half.