In a medium saucepan, combine cornmeal, sugar, and salt. Stir in milk. Add 1/2 cup butter. Cook and stir until thickened and bubbly. Reduce heat; cook and stir for 2 minutes more.
Transfer to very large mixing bowl, and cool until lukewarm (105 degree F to 115 degree F).
Dissolve yeast in the warm water. Add to cornmeal mixture, along with eggs, and stir well. Cover and let rise in a warm place for 1 hour or till bubbly.
Stir as much of the flour into the cornmeal mixture as you can with a wooden spoon. Turn the dough out onto a lightly floured surface. Knead in enough of the remaining flour to make a moderately stiff dough thats smooth and elastic (6 to 8 minutes total).
Shape dough into a ball. Place in a lightly greased bowl, turning once to grease surface of the dough. Cover and let rise in a warm place until almost doubled in size (for 45 to 60 minutes).
Punch dough down and turn out onto a lightly floured surface. Divide in half. Lightly roll one portion at a time to 1/2-inch thickness. Cut the dough with a floured 2-1/2- to 3-inch biscuit cutter. Reroll scraps and cut remaining rolls.
Place rolls, with sides touching, on a large greased baking sheet. Cover and let rise in a warm place until nearly doubled in size (for 30 to 45 minutes). Brush tops of rolls with melted butter.
Bake in a 375 degree F oven for 12 to 15 minutes or till golden. Serve warm.