Preheat oven to 400 degrees and spray a mini muffin pan with cooking spray.
In a large bowl, whisk together cornmeal, flour, baking powder, salt, sugar, and rosemary.
In a medium bowl, whisk together eggs, buttermilk, and butter until blended. Make a well in center of dry ingredients and pour egg mixture into well.
Fold dry ingredients into wet until blended with no lumps, but do not overmix.
Spoon batter into 16 mini-muffin cups, just enough to cover the bottom. Place one piece of cheese in each muffin cup. Spoon remaining batter on top of cheese. (Note- based on the size of your muffin tin, you may come out with more or less than 16 muffins.)
Place in oven and bake for 10-12 minutes, or until firm when lightly pressed on. Place pan on a wire rack and let cool for 5 minutes. Serve warm.