In a bowl, combine 3 cups of flour, cornmeal and yeast. In a small saucepan, heat milk, butter, sugar and salt until a thermometer reaches 120°-130° (butter does not need to melt). Blend into yeast mixture on low just until moistened. Add eggs; beat on low for 30 seconds. Beat on high for 3 minutes. Stir in enough remaining flour to form a stiff 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 1-1/4 hours. Punch dough down; knead four to five times. Shape into two loaves and place in greased 8x4-in. loaf pans. Cover and let rise until doubled, abut 30 minutes. Brush with butter.
Bake at 375° for 30 minutes. Remove from pans to cool on wire racks.