Start sourdough starter at least 3 days before baking: Combine the cold water, rye flour, and yeast in a bowl. Mix well; it will be lumpy. Pour the mixture in a clean bowl, cover with a cloth, and refrigerate for 3 days.
Remove the starter from the refrigerator 2 hours before beginning to make the bread.
Transfer the starter to a large bowl and add the warm water, yeast, flours, salt, cornmeal and caraway seeds and mix until smooth, 5 minutes.
Divide the dough in half. Shape into 2 even rounds. Place each round in a lightly greased bowl, cover with a clean cloth, and set aside to rise in a warm place until doubled in size, about 1-2 hrs.
Place a roasting pan on the bottom of the oven and fill with hot water. Preheat the oven to 400F. Sprinkle a baking sheet with corn- meal.
Dampen your hands and reshape the bread into even round mounds. Place the loaves on a prepared baking sheet. Bake the bread until crusty, about 2 hours. If the water in the roasting pan runs low during the baking, replenish it to provide the bread with steam heat. Cool, or serve warm.
Makes 2 large loaves.
Source: New York Cookbook, Molly O'Neill, 1993