Add the milk, water, butter, salt, onion powder, 1/2 cup of the sauteed onion, flour and yeast into the pan of a bread machine in the order recommended by the manufacturer. Select the dough cycle, and press start.

When the cycle has finished, remove the dough from the pan. Knead on a lightly floured surface. Cut into 8 equal pieces & form into balls & gently flatten with your hands. If they keep shrinking back, just let them relax for a minute before flattening. Place on a baking sheet, and cover loosely with a towel. Set in a draft-free place to rise until doubled in size, about an hour.

Preheat your oven to 350 degrees. Whisk together the egg white & water. Lightly brush each risen roll with the mixture. Sprinkle with the remaining 1/4 cup sauteed onion.

Bake for 15 minutes, or until golden brown.