Dissolve the yeast and honey in the warm water, and allow the mixture to proof for 4 or 5 minutes. Combine the warm milk and hot water with the softened butter and add to the yeast mixture along with the salt and caraway seeds. Add the flour, 1 cup at a time, stirring well after each addition. When you have added about 4½ cups the dough will become difficult to stir and will be quite sticky, but continue to add the remaining flour a tablespoon at a time. Scrape out the dough onto a floured board, and using a baker’s scraper or a large metal spatula, scrape under the dough and flour and fold the dough over. Continue to lift and fold, and with your free hand start pressing down and away from you on these folded areas, adding more flour as needed to dust your hands and to sprinkle the board. After 2 or 3 minutes of this procedure you can eliminate the scraper. Flour both hands and knead for about 10 minutes, until the dough is soft, velvety, and elastic.

Shape the dough into a ball and place in a well-buttered bowl, turning to coat with the butter. Cover with plastic wrap and place in a warm, draft-free area to double in bulk, which will take from 1 to 2 hours. Punch down, turn out on a lightly floured board, and divide into two equal pieces. Let the dough rest 2 or 3 minutes, and then shape into two loaves, either free form or for well-buttered 8× 4× 2-inch loaf pans. If you are making free-form loaves allow them to rise, covered, on a buttered baking sheet sprinkled with cornmeal until almost doubled in size, and then quickly invert them and brush with the egg white and water mixture. Otherwise, let the loaves rise, covered, in their pans until they have doubled in bulk and then brush the tops with the egg white and water mixture. Bake at 400° from 45 to 50 minutes or until the loaves sound hollow when tapped with the knuckles. Cool thoroughly on racks before slicing.