The temperature is too high, generally small bread should be baked at least 8~10 minutes, to adjust the temperature.
If you can't adjust the temperature, after the bread is colored, it will only take 1~2 minutes to cover the top with a piece of white paper to delay the coloring, and add a plate underneath to delay the coloring on the bottom.
It has nothing to do with greasing and egg wash, the more egg wash the deeper the color ~!