Step 1In the bowl of a stand mixer, combine the bread flour, whole-wheat flour and yeast. Stir together the honey and water and add to the flour mixture. Whisk until very smooth, about 2 minutes, until the sponge is the consistency of a thick batter. Scrape down the sides of the bowl. Set aside, covered with plastic wrap.
Step 1In a bowl, stir together the bread flour and the yeast. Gently scoop it onto the sponge to cover it completely. Cover with plastic wrap and allow to ferment for 1 to 1 1/2 hours in a warm place. (The sponge will bubble through the flour mixture.)
Step 2Place the bowl on the mixer and, using the dough hook, mix at low speed for about 1 minute, until the mixture forms a rough dough. Scrape down any bits of dough. Cover with plastic wrap and allow the dough to rest for 20 minutes.
Step 3Sprinkle in the salt and, using the dough hook, knead the dough at medium for about 7 minutes, until it is very elastic, smooth and slightly sticky. If it is too sticky, knead in a little flour. If it is not at all sticky, spray it with a little water and knead it in.
Step 4Using an oiled spatula or dough scraper, scrape the dough into an oiled large bowl and turn the dough to lightly coat it with oil. Cover with plastic wrap. Allow the dough to rise in a warm (75- to 80-degree) place until doubled in bulk, about 50 to 60 minutes.
Step 5Punch the dough down and knead several times. Shape it into a ball. Add a little oil to the bowl. Return the dough to the bowl and turn it to coat with oil. Cover and allow it to rise again until doubled, about 45 minutes to 1 hour.
Step 6Turn the dough out onto a lightly floured work surface and press it down to flatten slightly.
Step 7To make two free-form round loaves, cut the dough in half. Cover one half with plastic wrap. Knead the other half by hand for about 7 minutes, working one-half cup each of the ham and cheese into the dough throughout the kneading process. Shape into a ball and set it on an oiled baking sheet. Repeat with the remaining dough, ham and cheese.
Step 8Cover the shaped dough with a large container or oiled plastic wrap and allow it to rise until almost doubled, 45 minutes to 1 hour.
Step 9Place an oven rack at the lowest level and place a baking stone on it. Place a sheet pan on the floor of the oven. An hour before you plan to bake, heat the oven to 475 degrees, allowing the stone to get very hot.
Step 10With a sharp knife, make several half-inch-deep slashes in the top of the dough to make a cross-hatch pattern. Mist the dough with water and quickly set the dough, on its baking sheet, on the hot stone. Toss one-half cup of ice cubes onto the pan on the floor of the oven and immediately shut the oven door.
Step 11Bake the bread, one loaf at a time if necessary, for 10 minutes. Reduce the heat to 425 and continue baking for 20 to 30 minutes, rotating the pan after 10 minutes. Bake until the bread is brown and a skewer comes out clean; an instant thermometer will register 200 degrees.
Step 12For an extra-crisp crust, transfer the bread from the baking sheet to the stone and leave it in the oven for an extra 5 to 10 minutes with the door ajar. Remove the bread from the oven and transfer it to a wire rack. Let cool completely.