Combine 1/4 teaspoons yeast and 1/4 cup warm water, let stand about 5 minutes, until dissolved. Mix in 3/4 cup flour until completely moistened. Gather into a ball and put into a glass bowl, cover with plastic wrap and let sit for 3 - 5 hours, until very bubbly and tripled in size.
To mix dough, combine 1 teaspoons yeast in 1/4 cup warm water until dissolved, about 5 minutes.
Place biga in a large bowl, add 1/4 cup ice cold water and mix on low speed with paddle until smooth, add yeast mixture, salt and remaining 3/4 cup ice cold water, mix until blended. Add 2 3/4 cups flour and beat on medium speed until well blended. Change to dough hook and beat on medium speed until very smooth and elastic, about 12 - 15 minutes (dough will be very sticky).
Scrape dough into an oiled 2 quart bowl, wrap with plastic wrap and let rise until tripled in size, about 3 hours.
Sprinkle board generously with flour and scrape dough onto it. With floured hands, gently fold in half and pinch a seam, turn over and form into a 12 - 13 inch smooth log. Lightly sprinkle with flour, cover loosely with plastic wrap and let stand until puffy, about 30 minutes.
While dough is rising, place a large baking stone (or large baking sheet) in oven and set to 425°F, let heat at least 30 minutes. Flour a 14" x 17" piece of stiff cardboard or unedged baking sheet and gently lift dough onto it, stretching dough out to about 16 inches long. Shake floured board or sheet to slide dough diagonally onto baking stone or baking sheet.
Bake until deep golden brown, about 30 - 35 minutes. Cool on wire rack.
Times are approximate, altogether the bread takes most of the day to complete.