Combine first 3 ingredients in a saucepan; heat to 120° to 130°.
Combine 1 2/3 cups bread flour and next 4 ingredients in a large mixing bowl. Gradually add honey mixture and eggs, beating at low speed with a heavy-duty electric mixer until blended. Beat at medium speed 3 more minutes. Gradually stir in wheat flour and enough remaining bread flour to form a soft dough.
Turn dough out onto a well-floured surface. Knead until smooth and elastic (about 10 minutes). Place in a well-greased bowl, turning to grease top.
Cover and let rise in a warm place (85°), free from drafts, 1 hour or until doubled in bulk.
Punch dough down; let rest 15 minutes. Divide in half, shaping each portion into 2 small balls. Place 2 balls, side by side, in each of 2 well-greased 9- x 5-inch loafpans.
Cover and let rise in a warm place, free from drafts, 20 minutes or until doubled in bulk.
Combine egg white and 1 tablespoon water; brush on tops of loaves.
Bake at 375° for 35 to 40 minutes or until loaves sound hollow when tapped. (Cover with aluminum foil the last 15 minutes to prevent excessive browning, if necessary.) Remove from pans immediately; cool on wire racks.
Honey-Oat Buns: After letting dough rest, divide into 12 portions; shape into buns. Place on greased baking sheets. Cover and let rise 20 minutes or until doubled in bulk. Bake at 375º for 15 minutes. Yield: 1 dozen.