1. In large bowl, combine rye flour, unprocessed bran, wheat germ, and 3 cups whole wheat flour. In another large bowl, combine sugar, salt, yeast, and 3 cups flour mixture. In 2-quart saucepan over low heat, heat milk, butter or margarine, molasses, and 1 cup water until very warm (120° to 130°F.). Butter or margarine does not need to melt.
2. With mixer at low speed, gradually beat liquid into dry ingredients just until blended. Increase speed to medium; beat 2 minutes, occasionally scraping bowl with rubber spatula. Reserve 1 egg white; beat in remaining egg and egg yolk and 2 cups flour mixture; continue beating 2 minutes, scraping bowl often. With spoon, stir in remaining flour mixture and 3/4 cup whole-wheat flour to make a soft dough.
3. Lightly sprinkle work surface with whole wheat flour; turn dough onto surface and knead until smooth and elastic, about 10 minutes, working in more whole-wheat flour (about 1/2 cup) while kneading. Shape dough into ball; place in greased large bowl, turning dough to grease top. Cover; let rise in warm place (80° to 85°F.) until doubled, about 1 hour.
4. Punch down dough; turn onto surface lightly floured with whole-wheat flour; cover and let rest 15 minutes. Sprinkle cookie sheet with cornmeal.
5. Shape dough into oval loaf, tapering ends; place on cookie sheet. Cover; let rise in warm place until doubled, about 1 hour.
6. Preheat oven to 350°F. Cut 3 diagonal slashes on top of loaf. In cup, mix reserved egg white with 1 tablespoon water; brush over bread; sprinkle with caraway seeds. Bake loaf 50 to 60 minutes, until loaf tests done. Remove loaf from cookie sheet and cool on rack.