Add the first 9 ingredients to a 1-1/2- or 2-pound bread machine according to the manufacturer's directions. Select the dough cycle. When cycle is complete, remove dough. Punch down. Cover and let rest for 10 minutes.
Divide the dough into thirds. On a lightly floured surface, roll each portion into a 14x10-inch rectangle. Using a pizza cutter or sharp knife, cut the dough lengthwise into 1/2-inch-wide strips. For each breadstick, pick up 2 strips together and twist several times; press ends together. Place breadsticks 1/2 inch apart on greased baking sheets. Stir together egg white and water; brush onto breadsticks. Sprinkle with pepper, salt, or cheese.
Bake in a 400 degree oven for 10 to 12 minutes or until golden brown. Remove from baking sheets; cool on wire racks.