Add ingredients to bread machine pan according to manufacturer's directions.
Select dough cycle.
Scrape dough onto a board coated generously with bread flour. Taking care not to puncture or tear dough surface (interior is sticky), pat dough gently with floured hands to form a round loaf about 8 inches wide; do not knead. Sprinkle 2 tablespoons bread flour over dough.
Slide a pastry scraper or wide spatula under loaf to loosen, then lift quickly and carefully onto a buttered 14- by 17-inch baking sheet. Pat to reshape loaf, if necessary.
Lightly cover loaf with plastic wrap and let stand until puffy, about 30 minutes. Remove plastic.
With a floured razor blade or very sharp knife, cut 2 to 3 slashes about 1/2 inch deep across top of loaf.
Bake in a 425º oven until richly browned, 25 to 30 minutes.
After loaf has baked 25 minutes, sprinkle and additional 1/4 cup shredded dry jack or parmesan cheese over it, then continue to bake as directed.
Transfer loaf to a rack to cool at least 15 minutes before slicing. Serve hot, warm, or cool.
To make a 2-pound loaf, use 1 1/3 cups water, 1 1/3 cups sourdough starter, 4 cups bread flour, 2/3 cup rye flour, 4 teaspoons sugar, 1 teaspoon salt, and 1 package active dry yeast, 1/2 cup shredded dry jack or parmesan cheese, and 1/3 cup minced fresh jalapeño chilies.