Preheat oven to 400 degrees F. Line a 12 count muffin tin with paper liners or grease thoroughly with some extra butter.
Whisk together the melted butter, oil, eggs, honey and buttermilk and set aside.
In a large mixing bowl, stir together flour, cornmeal, sugar, brown sugar, baking powder and salt. Stir for at least two minutes or until very evenly blended.
Add the dry mixture to the wet mixture and stir just until blended.
For slightly taller muffins you can let the batter stand for 15 minutes.
Divide batter between muffin cups (cups should be about ¾ full) and bake for about 15 to 18 minutes or until edges are brown.
Let the muffins cool in the pan for about 5 minutes, then carefully remove and let cool completely.