Preheat your oven to 375 degrees F and grease an 8x8 baking dish. Set aside.
In a large saucepan, combine the milk, cornmeal, salt and pepper over medium heat. Bring to a boil, whisking constantly. Once the cornmeal reaches a boil, lower the temperature to low and continue to cook for 15-20 minutes, stirring frequently until the cornmeal has thickened substantially. Remove from heat and transfer to a large bowl.
While your cornmeal is cooking, heat the olive oil in a non-stick saute pan over medium heat. Add the jalapeños (optional) and green onion and season with salt and pepper. Cook for 4-5 minutes or until tender. Remove from heat and add to the bowl with the cooked cornmeal. Add the corn kernels and the butter to the bowl, and stir everything together to combine.
Now, one at a time add the egg yolks to the cornmeal, stirring in each egg yolk completely before adding the next one. Stir in the sharp white cheddar cheese then set the bowl aside.
Using a hand mixer or stand mixer (with whisk attachment fixed), beat your egg whites into stiff peaks. Fold the eggs whites very gently into the cornmeal mixture until the ingredients are combined, but not over mixed. Pour the batter into your prepared baking dish. Bake at 375 degrees F for 25-30 minutes or until it has puffed up and browned slightly. Remove from oven, garnish with green onions and more grated white cheddar if you wish, and enjoy!