How can I make whole grains stick to the top of bread? I want to bake bread or bagels that have whole grains like poppy seeds, cumin, caraway, etc. stuck to the top.

I have tried just pressing them to the top but they fall off during or shortly after baking. I tried an egg wash but I don't want my bread to have an eggy surface.

Does my dough need to be wetter? Do I need to water down my egg wash more? Or is there a better way entirely?
Use a boiled cornstarch wash for an in oven glue

Egg wash is a great glue, but generally lets go again when heated in the oven. Best used after baking not before