In a glass measuring cup, combine 1 cup warm water, 3 tablespoons warm milk, 1 1/2 tablespoons active dry yeast, and about 2 tablespoons honey. Let it sit undisturbed until foamy, about five minutes.
Beat 1 of the eggs in a separate bowl.
In a large mixing bowl, whisk together 2 cups of bread flour, 1 3/4 cups yellow cornmeal, and a pinch of kosher salt. Incorporate the softened 2 1/2 tablespoons of salted butter into the flour mixture.
Add the yeast mixture, the beaten egg, and the remaining honey into the flour mixture. Stir until a dough forms. The dough should be slightly sticky but cohesive.
Transfer the dough onto a clean, well-floured countertop. Knead the dough until it becomes smooth and elastic, about 8 to 10 minutes. Alternatively, use a stand mixer fitted with a dough hook.
Grease a large bowl and shape the dough into a ball. Place it in the bowl and cover it with plastic wrap. Let it rise in a warm place until doubled in size, about one to two hours.
Line two baking sheets with parchment paper. Divide the dough into 8 equal balls and gently roll them into balls. Arrange them on the prepared baking sheets.
Preheat the oven to 400° F and brush the tops with the egg wash. Bake until golden brown, about 15 minutes.
Once baked, allow the buns to cool completely. Brush with butter and honey if desired.
