Preheat oven to 350. If using iron skillet to bake cornbread, lightly coat it with oil and place in oven to warm. Otherwise, line muffin tins (or mini muffin tins) with liners - or grease and flour them well.

Combine milk and vinegar to as a buttermilk substitute. Allow to sit for at least 5 minutes. (You can just use buttermilk if you have it, and leave out the vinegar.) 

If using polenta, grind it in spice grinder 10-15 seconds to break it down finer into cornmeal. Combine cornmeal, corn flour, sugar, baking powder, baking soda and salt in bowl. Whisk together well.

Whisk in beaten eggs, melted butter, and milk + vinegar. Batter will not be runny, but not incredibly thick either.

Pour into heated skillet or spoon into prepared muffin tins. Bake for about 25 minutes or until the top starts to turn a golden brown. (I would check on it after 20 minutes.)