Pour 2 1/2 cups flour into a large bowl and make a well. Pour yeast, sugar, and two tablespoons of warm water (the water comes from the 1 cup listed above) in the well. Mix yeast, sugar and water carefully within the well. 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 out on counter top and knead until smooth. Add the remaining 1/2 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 for 15 to 20 minutes until golden brown.
Joyce's notes: I made the following changes and mixed on the dough cycle in my Zoji. I used 3 cups of flour and increased the water to 1 1/8 cup.