In a large mixing bowl, dissolve yeast and sugar in warm water. Let sit until creamy, about 10 minutes.
Mix in butter, salt and 1/3 of the flour. Beat with dough whisk or heavy spoon for 2 minutes. Fold in egg whites. Gradually add flour a little at a time, until dough forms a mass and begins to pull away from bowl.
Turn onto a floured surface. Knead, adding more flour as necessary, for 8 to 10 minutes, until smooth and elastic with bubbles.
Lightly oil a large mixing bowl, place the dough in the bowl and turn to coat with oil. Cover with a damp cloth and let rise in a warm place until doubled in volume, about 1 hour. Deflate the dough, form into a round and let rise again until doubled, about 45 minutes.
Preheat oven to 220 C / Gas mark 7. Deflate the dough and turn it out onto a lightly floured surface. Divide the dough into 24 equal pieces and form into oval rolls about 9cm (3 1/2 in) long. Place on lightly greased baking trays, cover and let rise until doubled in volume, about 40 minutes.
Place an empty baking tray on the bottom shelf of the oven. In a small bowl, lightly beat the egg white with the 2 tablespoons of milk to make the egg wash. Lightly brush the risen rolls with the egg wash. Place a cupful of ice cubes on the hot baking tray in the oven and immediately place the rolls in the oven.
Bake for about 20 minutes or until the tops are golden brown. Remove to a wire rack and cool.