1) To make the starter: Mix the starter ingredients together, cover, and let rest at room temperature overnight. Note: This is a dry, stiff starter. If it's too dry to come together, it may be that you measure your flour differently than we do here at King Arthur, or that you're in a particularly dry climate. Dribble in sufficient water to make the dough come together, and proceed with the recipe as directed.
2) To make the dough: Combine the starter with the remaining dough ingredients, and mix and knead — by hand, mixer, or bread machine set on the dough cycle — to make a soft, smooth dough.
3) Place the dough in a lightly greased bowl or large (8-cup) measure; cover, and let it rise for about 90 minutes, till it's just about doubled in bulk.
4) To make one large loaf: Gently deflate the dough, and divide it into three equal pieces. Shape each piece into a rough log, and let the logs rest, uncovered, for about 10 minutes. This gives the gluten in the dough a chance to relax, which in turn will make the logs easier to roll.
5) Working on a lightly greased surface, roll each log into a rope about 24" long. Brush each rope with the egg white/water, and sprinkle heavily with the sesame seeds, rolling the ropes gently in the seeds to pick up as many as possible.
6) Grab one end of each rope, and squeeze the ends together firmly. Braid the ropes, tucking the ends under to make a neat braided loaf.
7) To make rolls: Follow the directions above, but divide the dough into six pieces, rather than three. Roll each piece into a thin rope about 28" long. Take three of the ropes, and coat with seeds and braid as directed above. Repeat with the remaining three ropes. The resulting loaves will be about 18" long.
8) Cut each braid into six 3" rolls. Squeeze the cut ends together to seal, and tuck them under.
9) Place the loaf on a large, parchment-lined (or lightly greased) baking sheet. Or space the rolls on a baking sheet. Cover the loaf or rolls with lightly greased plastic wrap, and allow to rise till very puffy, about 90 minutes. Towards the end of the rising time, preheat the oven to 425°F.
10) Bake the loaf for about 25 to 35 minutes, till it's a deep golden brown. The rolls will need to bake for about 25 minutes. Remove from the oven, and cool on a rack.
Yield: one large loaf, or 12 rolls.