Egg proteins coagulate to form bonds with each other as the temperature rises during baking. When a bread dough is lacking in fat, the sugar molecules will scatter throughout the egg proteins and slow down their coagulation during baking. By surrounding the egg proteins and interfering with their ability to form bonds, sugar increases the temperature at which egg proteins coagulate. As a result, a rich bread dough contains both eggs and fat to allow it to set, or form its desirable, solid, screenlike texture at a temperature that doesn’t cause the crust to brown too quickly.