Preheat the oven to 400 degrees. Lightly mist a Madeleine mold or mini muffin tin with non-stick spray. Set aside.
In a medium bowl, whisk together flour, cornmeal, sugar, baking powder, salt, and cheese until combined.
In a separate bowl {or in a stand mixer fitted with the whisk attachment}, beat eggs until pale and slightly frothy.
Add about half the dry mixture to the eggs, and fold it in gently with a silicone spatula until it just disappears. Fold in the remaining dry ingredients just until everything is moistened. The batter will be thick.{Don't overmix.}
Pour in the melted butter and fold it into the batter gently. Once it is fully incorporated, add the milk and fold it in as well. The batter will look kind of ugly and curdled -- it's supposed to look that way.
Scoop batter into the prepared Madeleine mold, filling each cavity to just under the top. {They will puff up as they bake so don't overfill.}
Bake for about 12 to 14 minutes or until the tops are golden and the edges are slightly browned.