Lightly grease a shallow ovenproof, sided dish (about 28cm/11in diameter). Pre-heat the oven to 180C/350F/Gas 4.
Lightly whisk the egg and caster sugar together in a bowl.
Add the mascarpone and whisk again until smooth and there are no lumps.
Arrange the brioche slices as neatly as possible in a single layer on the greased tart plate to completely cover the plate.
Trim the brioche slices as necessary to fit. Spread the mascarpone mixture over the brioche slices to about 1cm/½in away from the edge. You don't have to be accurate about this!
Arrange the apricot halves neatly in a spiral over the mascarpone right to the edge of the brioche. Sprinkle the demerara sugar over the apricots.
Bake in the pre-heated oven for 30-35 minutes until the custard is set and golden.
Serve immediately with créme fraïche and dust with icing sugar.