In stand mixer bowl, add 1 1/2 cups flour, yeast, cornmeal, sugar and salt; mix well. In saucepan or microwave-safe dish, heat milk, water and 2 tablespoons butter until warm (120-130°F; butter does not need to melt). Add to flour mixture. Using a paddle attachment, blend on low speed for 30 seconds. Beat on medium speed for 3 minutes.
Switch to dough hook attachment. Gradually stir in cheese and enough remaining flour to make a firm dough. Knead until smooth and elastic, about 5 to 8 minutes.(NOTE: For hand mixing: following above steps, mix ingredients in large mixing bowl using a wooden spoon or dough whisk. Knead on floured surface until smooth and elastic.) Place dough in lightly oiled bowl and turn to grease top. Cover; let rise until indentation remains after poking dough with finger down to second knuckle, about 1 hour.
Punch down dough and turn out on lightly floured surface; divide into 4 parts. Divide each fourth into 10 pieces. Shape each piece into a smooth ball; dip in melted butter. Place in greased 10-inch solid bottom tubed cake pan or a 12-cup Bundt pan. Cover; refrigerate 2 to 24 hours.
Take pan out of refrigerator. Preheat oven to 375°F.
Bake for 55 to 60 minutes until golden brown. Remove from pan; brush with butter. Serve warm.