Put all dough ingredients into bread maker.
Set bread machine to dough setting. (This will take about 1 & 1/2 hours)
NOTE: after the first few minutes of the machine kneading the dough, check that the dough isn't sticking to the sides of the bread maker and has formed a 'ball'. If the dough is sticking, add a tablespoon of flour, let it knead and gradually add more if needed. The dough should come together without sticking to the pan.
When dough is ready, remove it from Bread Maker. Place dough on counter that's lightly dusted with flour and gently fold it several times.
Form into a roll, about 12 - 16 inches long and then cut into 12 sections.
Form each piece into a ball and place onto 2 lightly greased baking sheets. Cover and let rise until double in volume, about 45 minutes.
About 15 minutes before baking, preheat oven to 425°F. Place an empty baking sheet on bottom rack.
When oven is hot, gently brush rolls with egg wash (mixing 1 egg white with 2 tbsp milk). Cut a fairly deep slash in top of each roll with very sharp knife.
Place 1 cup of ice cubes on the hot baking sheet in oven just before placing baking sheets with rolls into oven.
Bake for about 18 - 20 minutes or until tops are nicely browned. Be careful when removing the rolls from the oven ... there may be steam that escapes when you open door (from ice cubes).
Remove to rack and let cool for about ½ hour before serving.