In a bowl of a standing electric mixer fitted with a dough hook, combine 3 cups of the bread flour with the whole-wheat flour, yeast and salt.
In a pitcher, stir together the Sourdough Starter, water, beer, olive oil and milk. With the mixer set at low speed, gradually pour in the liquid, then increase the speed to medium and knead for 7 minutes. Stop the machine occasionally to scrape down the inside of the bowl with a spatula. The dough will be sticky.
Spread 1/2 cup of the bread flour on a work surface. Scrape the dough onto the surface and knead vigorously by hand for 5 minutes, using just enough additional flour to prevent the dough from sticking. Transfer the dough to a lightly oiled large bowl; turn the dough to coat it with oil. Cover the bowl with plastic wrap and leave it in a warm place until the dough has doubled in bulk, 2 1/2 to 3 hours.
Turn the dough out onto a freshly flour surface, knead it briefly and shape it into an oval. Sift 2 tablespoons of the bread flour over a large baking sheet, then sprinkle it with the cornmeal. Transfer the dough to the sheet and gently stretch it into a long flat loaf about 2 inches high. Dust the rough surface of the leaf lightly with more of the bead flour, cover with a linen dish town and let rise at room temperature for 2 hours.
Meanwhile, preheat the oven to 450° and position a rack in the lower third of the oven. With a knuckle, indent the dough in 6 spots. Bake the bread for 30 to 35 minutes, or until golden brown.
In Step 3, the dough can rise overnight in the refrigerator.