In a small saucepan over low heat, warm the butter, honey and milk. Heat until butter is melted and mixture is smooth. Remove from heat and let cool for 5 minutes, or until 120-130°F.
In the bowl of a stand mixer fitted with a dough hook attachment, combine the cornmeal, 1 1/2 cup of the all-purpose flour, salt and yeast. Add the warm milk mixture and mix until combined.
With the mixer on medium low speed, add the remaining all-purpose flour 1/4 cup at a time until dough clears the bowl and is only slightly sticky to the touch (you may not need the full 3 cups of flour). Continue to knead until smooth and elastic, about 5-7 minutes.
Place dough in a greased bowl and cover with plastic wrap. Let rise in a warm place until doubled, about 1 hour.
Gently punch down dough and knead a few times, then let rest for about 5 minutes. On a clean surface, roll out the dough into a long rectangle about 8 inches wide. Starting on a short side, roll up the dough and place seam-side down in a greased 9x5-inch loaf pan.
Cover with plastic wrap and let rise until doubled again, about 30 minutes. Meanwhile, preheat oven to 375°F.
Bake until the top is golden, about 40-45 minutes. Brush with the warm loaf with melted butter. Serve warm or at room temperature.