For the Biga: Mix all of the biga ingredients in a medium-sized bowl until well-blended. Cover the bowl, and leave it at cool room temperature for 12 to 20 hours, until the biga is very bubbly.
For the Dough: Mix the biga and the remaining dough ingredients, except the cheese, using an electric mixer set on slow speed, for 2 to 4 minutes. Increase the speed to medium and mix for about 4 minutes; the dough should be soft and slightly sticky. Add additional water or flour if necessary. Do not over add flour, the dough should be very soft.
Mix in the cheese; be aware some of the cheese will fly out. Just pick them up and put them back in the bowl. Allow the dough to rise, in a greased, covered bowl, for 1 to 2 hours, until it's very puffy. Note: You can also mix this dough in a bread machine set on the dough cycle; add the diced cheese several minutes before the end of the final kneading cycle.
Turn the dough out onto a well-floured surface and shape it into two long loaves, about 12 x 4 inches each, or 4 loaves, approx 6x4 inches. Place the loaves, floured side up, onto parchment paper lined baking sheets. Cover the loaves with a proof cover or well-greased plastic wrap and allow the loaves to rise for 45 minutes or until they're very puffy. Sprinkle loaves with additional grated cheese.
Bake the ciabatta in a preheated 450 oven for 22 to 26 minutes, until it's golden brown. Remove from the oven and cool on a rack.