In the bowl of an electric stand mixer fitted with the dough hook, combine 2½ cups all-purpose flour, ½ cup plain cornmeal, 2 tbsp sugar, 1 (¼-oz) package active dry yeast, and 1 tsp salt. Mix on low speed until the dry ingredients are well combined.
In a small saucepan, heat 1 cup water and 2 tbsp butter until warm, about 120° to 130°F. Add this warm liquid to the dry ingredients in the mixer bowl.
Beat the mixture until it is moistened and starts to come together. The dough should be slightly sticky.
Add 1 egg to the bowl and beat on medium speed for 5 to 6 minutes until the dough is smooth and elastic.
Cover the mixing bowl with a clean kitchen towel and let it rise in a warm place until doubled in size, about 1 hour.
After it has risen, punch down the dough and turn it out onto a lightly floured surface. Divide it into 18 equal pieces and shape each piece into a ball.
Place the shaped rolls in a lightly greased 13×9-inch baking pan or 9-inch round cake pans. Cover and let rise until doubled, about 30 minutes.
Preheat your oven to 400°F and bake the rolls for 15 to 20 minutes or until golden brown.
Melt the remaining 1 tbsp butter and brush over the warm rolls before serving.
