A delicious New York Deli Rye Bread recipe, adapted from The Bread Baker's Apprentice.
Dice the onions and saute in oil until they sweat. Cool onions until they're no longer hot. Mix them into the starter, cover, and let dough ferment until it bubbles. (I did this in a warmed oven. It still took several hours.) Refrigerate overnight.
Remove the starter from the fridge 1 hour prior to making the dough. Combine starter with all remaining ingredients except water and egg white in the bowl of a stand mixer. Stir together. (Reinhart suggests with a wooden spoon or paddle attachment; I used the dough hook.) Add water as necessary to form a soft but not sticky dough. Let dough rest for 5 minutes to allow gluten to develop.