I did say I'd keep tinkering, and I have. Here is the new improved bread-machine brioche recipe. I'm very pleased with myself: this stuff is really good.
1 large egg or 2 medium eggs
1/4 tsp vanilla essence
cold milk
1/4 tsp salt
30g diced cold butter
15g brown sugar
35g-40g castor sugar
80g strong white bread flour, sieved
180g plain flour, sieved
for 1 large egg, use 2 3/4 tsp fast-acting yeast
for 2 medium eggs, use 1 tbsp fast-acting yeast
Beat the egg, add the vanilla, then add cold milk to bring the total amount of wet ingredients up to 150ml.
My experiments have shown huge (bad) differences with softened butter, and so I recommend not softening it, but dice it quite small.
I'm using setting 1 on a Morphy Richards machine, which is the setting for a basic small white loaf. To help you tally that with your machine, that is:
Slow knead: 6min
Fast knead: 27min
Rise: 23min
Shape: 20sec
Rise: 64min
Bake: 45min
I'm getting fat here.