Mix the biga ingredients in a small bowl until well combined. Let the biga rest overnight, covered, or for up to 15 hours., Place all of the dough ingredients, including the biga, into the bowl of your mixer, and beat it at medium speed (speed 4 on a KitchenAid), using the flat beater, for 3 minutes; the dough should have started to clear the sides of the bowl. If it hasn't, increase the speed of the mixer, and mix for an additional 2 minutes., Switch to the dough hook, and knead for an additional 3 to 4 minutes; the dough will be extremely soft., Transfer the dough to a lightly greased bowl, cover it, and allow it to rise for 2 hours, deflating it once midway through the rising time., Transfer the dough to a well-oiled work surface. Lightly grease a half-sheet baking pan (18" x 13") or similar large pan, and your hands., Using a bench knife or your fingers, divide the dough in half. Handling the dough gently, stretch one piece into a log about 10" long, and place it crosswise on one half of the baking sheet. Flatten the log with your fingers until it's about 3" wide., Repeat with the remaining piece of dough. Lightly cover the dough with heavily oiled plastic wrap, and allow it to rise for 2 hours; it'll become very puffy, and will jiggle when you shake the pan gently. Towards the end of the rising time, preheat the oven to 425°F., Bake the loaves for 22 to 25 minutes, or until they're golden brown., Turn off the oven, remove the panini loaves from the baking sheet, and return them to the oven, propping the oven door open a couple of inches with a folded-over potholder. Allow the loaves to cool completely in the oven; this will give them a very crisp crust. If desired, sift a dusting of flour on top of the cooled loaves.