For the ice cream, mix all of the ingredients together in a bowl and then churn in your ice cream maker. Place the frozen mixture into a freezer-safe container and store in the freezer until needed.
To make the pastry, cream together the soft butter and caster sugar. Add a pinch of salt, the plain flour and powdered bran flakes. Stir to combine. Add the beaten eggs and mix together to form a soft sticky dough. Cover with cling film and place into the fridge to rest for at least an hour.
Preheat the oven to 170C/340F/Gas 3½.
When the pastry is rested, lightly dust a work surface with flour and roll out the pastry to the thickness of a pound coin. Line a 23cm/9in loose-bottomed tart case with the pastry, gently pushing it into the edges and leaving any excess overhanging the sides.
Line the pastry with baking parchment. Fill with ceramic baking beans or uncooked rice and bake for 20-25 minutes. Remove the beans and lining paper, return it to the oven and cook for a further 10 minutes to ensure the pastry is cooked through and dried out. Remove from the oven and set aside to cool. Turn the oven temperature down to 160C/325F/Gas 3.
To make the filling, melt the butter in a saucepan over a medium heat until it foams and turns brown. Add the syrup, take the pan off the heat and whisk to combine (if the mixture is grainy pass it through a sieve). Put the brioche crumbs in a medium bowl and add the butter and syrup mixture. Whisk in the cream, salt, eggs and egg yolk and leave to cool for 10-15 minutes. Once cooled, pour the filling into the cooled tart case and bake for 25 minutes. Reduce the oven temperature to 140C/275F/Gas 1, and cook for a further 30 minutes, until the tart is just set – it should still have a wobble in the centre. Remove the tart from the oven and leave to cool and set for 30 minutes.
When ready to serve, sprinkle a little sea salt over the top of the tart, trim the top edges of the tart and release the ring. Cut into slices and serve with the mascarpone ice cream.