Churn mixed ice cream ingredients in an ice cream maker and freeze until needed.
Cream butter and sugar, then mix in salt, flour, bran powder, and eggs to form a dough.
Chill the dough in the fridge for at least one hour.
Preheat the oven to 170°C.
Roll out the pastry and line a 23cm tart case, leaving excess overhanging.
Blind bake with parchment and beans for 20-25 minutes.
Remove beans and bake for 10 more minutes to dry the pastry.
Cool the pastry and lower the oven temperature to 160°C.
Brown the butter in a pan, whisk in syrup, and combine with brioche crumbs.
Whisk in cream, salt, eggs, and yolk, then let the filling cool.
Pour filling into the case and bake at 160°C for 25 minutes.
Lower heat to 140°C and bake for 30 minutes until just set with a wobble.
Cool for 30 minutes, trim edges, sprinkle with sea salt, and serve with ice cream.