Pour 2½ cups flour into a large bowl and form a well in the center. In a separate container, mix yeast, sugar, and two tablespoons of water (the water comes from the 1 cup listed above ). Pour the yeast mixture into the well but do not mix with the flour at this time. Cover the bowl with a cloth and set it in a warm place for 15 minutes. Add the remaining water and oil and beat until mixed.
Turn dough out on counter top and knead until smooth. Add the remaining ½ cup flour as needed. Put dough in a bowl, cover, and let it rise until double in size. Punch down and divide the dough into 12 parts. Shape into oval rolls and place 3" apart on a greased and floured cookie sheet. Cover and let rise until double in size. Beat egg white and 1 teaspoon water with a fork until frothy and brush on the rolls.
Bake in a preheated oven at 450° F for 15 to 20 minutes until golden brown.