What would be the best way for replacing egg wash when baking bread?
I've tried unsweetened soy milk but it didn't brown that well.
You could always try using vegetable, corn, or light/regular olive oil, vegan margarine, or light corn syrup thinned with a bit of water (to prevent over browning):
I also saw something here that mentioned the use of soy milk, but you said it didn't brown well. If it didn't brown at all, then it is most likely because you were using unsweetened soy milk (remember, sugar browns when exposed to heat).
An effective method I've recently tried is using date honey, diluted with water or almond milk at a ratio of 1:1.
Another fine substitute is carob syrup, diluted similarly.
Due to the dark color of both ingredients, browning is guaranteed.
The two options also work well for browning grilled vegetables or tofu.
In Brazil friends use a mix of catchup, mustard and a bit of water to brush over savory dishes, it browns very well and gives a bit of flavor
The food industry has an answer: fructose syrup (or high-fructose corn syrup).
Apparently, when you're browning millions of baked goods a year, egg wash is expensive. Fructose syrup is much cheaper and more reliable.
Anyway, there is no reason it wouldn't work for a home baked loaf of bread.
A mixture of soymilk and agave syrup works beautifully! It gives a nice glaze and when we make bagels and brush them with the soymilk/agave before baking the seeds really stay on.
I would try some watered down vegan mayonnaise.
After reading all the comments suggesting various sugar syrups, I'm going to try watered down maple syrup.
I will try juicing the those fresh yellow beets then mix it in oil.