Preheat the oven to 400°F. Generously grease a 12-cup muffin pan with butter or shortening or fit with paper cups.
In a large mixing bowl whisk the flour, cornmeal, sugar, baking powder, baking soda and salt together.
In a separate bowl whisk the buttermilk, melted butter, oil, egg and egg yolk together.
Pour the wet ingredients over the dry and mix gently with a spoon until combined - a little lumpy is OK.
Stir in the corn and cheese.
Use an ice cream scoop to fill the muffins cups just shy of the top.
Bake 16 - 18 minutes or until a toothpick comes out clean. Cool in pan 20 minutes then turn out and cool completely on a wire rack.