Add one - third egg mixture to reserved chocolate mixture and stir to combine with a spatula. (epicurious.com)
Keep working and by the time you add the third egg it will start coming together again. (ovenloveblog.com)
I've tried a few things, including a third egg wash halfway through the baking time (this was to target the parts of the challah that weren't exposed until after the over spring) and mixing a little cream into the egg wash, but I've never been able to get them as brown (the bottom starts to burn) and definitely not as evenly brown as yours. (smittenkitchen.com)