Egg YOLK replacement?
In an article I with a very quick google search found here, it seems that you can


  blend 1 tablespoon of flax or chia seeds with 3 tablespoons of water until mixture is thick and creamy.


However, I suspect that this would add a gritty texture that would be unpleasant in easter sweet breads. You would probably find that a full-fat yogurt is a good alternative, having both protein and fats.

I also found this article, which uses chickpea flour, flour (wheat, rice, sorghum), water and oil.