Combine the starter, flours, honey, yeast, salt, and water in the mixer and mix on low with the paddle until the mixture comes together.
Switch to the bread hook and knead, adding more bread flour until the dough is workable. Knead for 5-8 minutes on medium.
Transfer to an oiled bowl, cover with a damp kitchen towel and let rise until doubled, 2 or so hours.
Work on a floured surface with a bread knife, tucking under and shaping and adding flour until you get something resembling a ball.
Transfer to a very well-floured 9″ banneton, seam-side up, cover with the damp kitchen towel and allow to rise for another hour, until the dough has reached the top of the banneton.
Preheat oven to 450˚F with a baking stone on the middle rack and a cast iron pan on the lower rack during this time.
Remove the towel, cover with parchment paper to invert onto a baking peel. The dough will spread out a bit.
Brush with the egg white wash and sprinkle with the remaining spent grains, then use a lame to score an X shape in the top of the dough.
Carefully use the peel to transfer the dough, parchment paper and all, onto the baking stone, mist the sides of the oven with a few squirts of water, and throw a half cup of ice into the cast iron pan.
Bake for about 35-40 minutes or until the bread feels hollow when rapping a knuckle on it.