In a large bowl, dissolve yeast in warm water. Add honey; let stand for 5 minutes. Add the beets, milk, butter, salt and 3 cups flour. Beat until smooth. Stir in enough remaining flour to form a soft dough.
Turn onto a floured surface; knead until smooth and elastic, 6-8 minutes. Place in a greased bowl, turning once to grease top. Cover and let rise in a warm place until doubled, about 50 minutes.
Punch dough down. Turn onto a lightly floured surface; divide dough in half. Shape into 2 loaves. Place in 2 greased 9x5-in. loaf pans. Cover and let rise until doubled, about 40 minutes.
Brush with egg white; sprinkle with sesame seeds. Bake at 350° until top begins to brown, 30-35 minutes. Remove from pans to wire racks to cool. If desired, serve with honey and butter.