Knead 2 cups of bread flour, ¼ teaspoon of yeast, and 1 cup of water on low until it forms dough. Move the dough to a bowl, cover it with plastic wrap, and let it rise for three hours (you should see bubbles). Refrigerate the biga for 8-24 hours.
Take the biga out of the refrigerator. Knead 3 cups of bread flour, 1 teaspoon of instant yeast, and 1 1/3 cups of water on low until it forms dough. Cover mixing bowl lightly with plastic wrap without removing the hook and let sit for 20 minutes. Add the biga and 2 teaspoons of salt to the bowl, then knead on low until a ball forms; increase speed to 2 and knead for another minute or so until dough is thoroughly combined. Move the dough to a large bowl and cover with plastic wrap.
Let the dough rise for three hours; after the first and second hour of rising, pull the dough from each side towards the center of the bowl. After the third hour, turn the dough out onto a floured surface and flour the dough. Press the dough into a large rectange (around 8" by 10"), fold the top corners of the long side towards the center, and roll the dough up from the top. Gently shape the dough into a loaf, move it to a sheet of parchment paper, dust with flour, cover it with plastic wrap, and let rise for another hour. Heat the over to 500F with a baking stone on the lower-middle rack.
When the hour is up, slash the top about ½ inch deep every 1½ inches or so; spritz the loaf with water. Bake for 10 minutes at 500F, turn the loaf around, and bake at 400F for 40 minutes or until the loaf reached 210 degrees. Let the loaf cool on a wire rack until it reaches room temperature.