In the bowl of a stand mixer, dissolve yeast in warm water. Let stand 5 minutes until foamy. Add honey, melted, butter, egg, and garlic mixing on low speed until smooth. Add salt, cornmeal, and 3-1/2 cups flour to bowl and increase speed to medium until dough pulls away from sides of bowl, adding more flour if necessary.
Knead dough on medium speed 4-5 minutes until dough is smooth and elastic. Remove from bowl and form into a ball. Place in a greased bowl, turning once to grease top. Cover with plastic wrap and let rise 1 hour or until doubled in size.
Punch dough down and remove from bowl. Divide into 12 equal pieces and roll each portion into a smooth ball. Place dinner rolls in a greased 9x13 baking pan and cover with plastic wrap. Let rise until rolls are doubled in size, about 30 minutes.
Bake rolls at 375F 20-25 minutes or until a deep golden brown. Remove from oven and set aside for a moment.