Remove the biga from the refrigerator 1 hour before making the dough. Cut it into about 10 small pieces with a pastry scraper or a serrated knife. Spray the dough with vegetable spray and cover with plastic wrap and let sit for 1 hour to take off the chill.
Whisk together the flour, salt, and yeast in the bowl of a stand mixer. Add the biga pieces, mashed potatoes, and 12 to 13 ½ oz. (1 ⅔ cup) water. Measure all of the water out but leave a Tablespoon or 2 in the measuring cup. Using the paddle attachment mix on low speed until the ingredients form a wet, sticky ball. If there is still some loose flour add the rest of the water in the measuring cup and continue to mix.
Switch to the dough hook and mix on medium speed for 4 to 5 minutes, or for as long as it takes to create a smooth, sticky dough. The dough will clear the sides of the bowl but it will stick to the bottom. The dough will be sticky -- the wetter it is, the better the final bread will be.
Sprinkle bread flour on the counter to make a bed.Using a scraper or spatula dipped in water, transfer the dough to the bed of flour and proceed with the stretch-and-fold method. This method entails (A) dusting the top of the dough liberally with flour, patting the dough into a rectangle. Wait 2 minutes for the dough to relax. Coat your hands with flour and (B) lift the dough from each end, stretching it to twice its size. (C) Fold the dough over itself, letter style to return to a rectangular shape. Mist the top of the dough with spray oil, again dust with flour, and loosely cover with plastic wrap.
Let it rest for 30 minutes. Repeat the stretch-and-fold method and again mist with spray oil, dust with flour, and cover. (Each time you repeat this process, the dough will become stronger, more elastic, and less sticky.)
Lightly oil a large mixing bowl. For the third time, repeat the stretch-and-fold technique. Transfer the dough to the bowl and cover the bowl with plastic wrap. Ferment the dough at room temperature for 2 hours.
Generously dust the counter with flour and transfer the dough to the counter, taking care not to degas the dough. With a metal pastry scraper or a serrated knife dusted with flour, divide the dough into 3 pieces.With floured hands, gently shape the dough pieces into 3 boules (balls). You do this by creating surface tension as you bring the opposite ends together to make a ball. Keep smoothing down the sides from top to bottom. Pinch to seal the bottom of the dough where the creases come together. Let them relax seam-side down on the counter while you prepare the 3 proofing bowls.
Coat the proofing bowl with spray oil and then line the bowl with a cloth napkin, or smooth towel. Spray the cloth with spray oil and dust with flour. (I have muslin-lined bannetons and for the third bowl I used a pastry cloth with a regular glass bowl) Gently transfer the dough, seam side up, into each bowls. If the seam opens up, pinch it closed. Mist the top of the dough with spray oil and cover the bowls with the flaps of the cloth or a smooth dish towel.
Proof at room temperature for 60 to 90 minutes, or until the dough has expanded to about 1 ½ times its original size.
Preheat the oven to 500 F. Have a water spray bottle ready.
Generously dust the back of a sheet pan with semolina flour or cornmeal. Spray a sheet of kitchen parchment with spray oil and put the parchment -- oiled side up -- on the sheet pan. Gently transfer the dough to the pan by carefully turning each bowl over onto the pan, lifting off the bowl, and then carefully peeling off the cloth. The dough will spread out on the pan. With a sharp razor blade or french lame, score the loaves with the pound (#) sign. Transfer the dough to the baking stone (or bake on the pan). After 30 seconds, spray the oven walls with water and close the door again. Be careful you don't spray the light!!!! Repeat twice more at 30-second intervals. After the last time lower the oven setting to 450 F and bake for 15 minutes. Check the loaves and rotate 180 degrees for even baking. Continue baking for 10 to 15 minutes or until the breads are a deep golden brown and the internal temperature registers 205 F.
Remove the loaves from the oven and transfer them to a cooling rack. Allow the loaves to cool for at least 40 minutes. This will be sheer torture!