You will need a 2 litre(70fl oz) gratin or other ovenproof baking dish.
Ideally the bread should be a day or two old but if not, before doing anything else, slice the bread and leave to dry for a while. Cut the crusts from the loaf (yielding 300–350g/10½–12oz) of bread and cut that loaf into 1cm (½in) slices. When ready to assemble the dish, spread the slices with butter, then cut from corner to corner, so portioning into triangles.
Put a saucepan of water on to simmer. Find a bowl that sits on top without touching the water. Add the chocolate, cream and rum. When it looks as though much of the chocolate has melted, begin to stir the pan with a spatula to encourage it further, and to create a dark, glossy cream. Remove the pan from the heat but keep the bowl resting on it.
Meanwhile, put the milk, cocoa powder and the dark brown soft sugar in a saucepan and gently bring to a simmer, stirring occasionally to ensure the sugar dissolves. As bubbles begin to appear around the edge, remove from the heat. In a mixing bowl, use a balloon whisk to beat the eggs and the caster sugar until light in colour and volume. Add a ladleful of the warm cocoa milk into the eggs, beat with the whisk to combine, then gradually pour the rest of the milk on top, whisking constantly. Add the chocolate cream and whisk to combine.
Pour the custard to 1cm (½in) deep in your baking dish. Arrange half the bread triangles in
one layer of overlapping scales and pour half of the remaining custard over the top, turning the bread brown. Sprinkle with half a teaspoon of salt, then crumble half the halva, dotting it into the natural crevices. Add another layer of bread, then the last of the custard, again colouring as much of the bread as you can. Press down with the back of a spatula or palette knife to further soak the bread, and spoon a little from between the gaps, onto any remaining white dots. Cover and refrigerate for 24 hours (it needs this time for the custard to fully soak into the bread).
To cook, heat the oven to 180°C/160°C fan/350°F. Drizzle the top of the pudding with the tahini, allowing it to form puddles in the Vs between the bread. Dot those puddles with thumbnail-size nuggets of the remaining halva, then sprinkle the remaining half a teaspoon of flaky sea salt from a height. Bake at the top of the oven for 30 minutes. The top will be crunchy but the underneath should still be luscious. Rest for 10 minutes before serving with cream and/or ice cream.