An egg wash is a glaze used to brown and shine the crust of breads and pastries. The more fat it contains, the darker the glaze will be. For a plain shine use water alone, egg white, or milk. A whole egg makes it more golden, and yolk and cream is even darker.
Washes without eggs are often used including straight cream, diluted honey, molasses or simple syrup (sugar water). Sugar can also be sprinkled on top of wash for added browning.
Every kind of wash can be made more fluid with a pinch of salt.
And use a brush to get the wash on evenly. It doesn’t have to be a fancy brush. Go the hardware store and get yourself a couple cheap 89-cent paint brushes. They come in handy for brushing oil on grilled foods and dusting flour off of things.