Place the milk, water, butter, salt, sugar, onion powder, 3 tablespoons of dried onion, potato flakes, 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 completed, remove the dough from the machine, and knead on a lightly floured surface
Cut into 8 equal pieces, and form into balls
Gently flatten the balls until they are 4 inches in diameter
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 40 minutes
Preheat the oven to 350 degrees F (175 degrees C)
Whisk together the egg white and water in a cup
Brush over the tops of the risen rolls, and sprinkle with remaining minced onion
Bake for 15 to 20 minutes in the preheated oven, until golden brown
Cool completely, then slice in half horizontally before using