1. Preheat the oven to 400 degrees F. Fill a regular-size muffin pan with paper muffin cups or spray with cooking spray. Set aside.
2. In a large bowl, whisk together the flour, cornmeal, sugar, baking powder, baking soda, salt, and fresh rosemary. Set aside.
3. In a medium bowl, whisk together the buttermilk, melted butter, oil, and eggs until well blended. Pour the liquid ingredients over the dry ingredients and mix with a rubber spatula until combined. Fold in the corn and cheddar cheese. Divide the batter evenly among the muffin cups.
4. Bake for 15 minutes, or until the tops are golden and a toothpick inserted into the center of the muffins comes out clean. Transfer the pan to a rack and cool for 5 minutes. Remove muffins from pan and serve.
Note-we used white cheddar cheese, but feel free to use your favorite cheddar.