Hmm probably the former actually. Recipe called for a 210 oven but I think I'll go a bit lower next time and keep the baking more consistent as it was a bit in/out when I realised it wasn't baked. Good shout on the shaping, did eggwash but I need one of those silicone brushes to get it on properly.
In the spirit of just recommending what you have: Kenwood Chef. But there are various iterations with various features and power.
P.s, good luck!
Brioche looked ok inside, quite doughy at the base in places probably a touch over proofed.