In a large bowl, dissolve yeast in warm water. Add the milk, butter, sugar, salt, eggs and 1 cup flour. Beat on low speed for 30 seconds. Beat on medium for 2 minutes. Stir in 1/2 cup cornmeal and remaining flour. Stir in chilies and cheese. Do not knead. Cover and let rise in a warm place until doubled, about 45 minutes.
Stir dough down. Sprinkle 3 teaspoons cornmeal into a greased 9x5-in. loaf pan. Spoon batter into pan. Sprinkle with remaining cornmeal. Cover and let rise in a warm place until doubled, about 30 minutes.
Bake at 375° for 45-50 minutes or until bread sounds hollow when tapped. Cool for 10 minutes before removing from pan to a wire rack. Store in the refrigerator.