8. If the bagel passes the test, dry the test bagel carefully and return it to the pan. Cover the pan and place it in the refrigerator overnight. 9. If the bagel doesn’t rise to the top, dry the bagel and replace it on the pan. Cover the pan and let the bagels rise for another 10 or 20 minutes and test again.
Brioche is really an egg bread, so it will be hard to replace it with an egg substitute and maintaining the texture and flavor. You can certainly try using an egg replacer, but I would make a small batch (cut the recipe by 1/4) and make sure you like it. There are other recipes in the book that don’t have eggs, but are sweet doughs, which may serve your purposes better.