Bring water to a boil and slowly whisk in corn meal. Let it simmer until it thickens.
Pour corn meal into a greased pan and spread evenly to approximately 3/8 of an inch thick. Let cool completely.
When cool, cut batons using a sharp knife. The batons should be about the length and width of your index finger.
In a bowl, mix the parmesan cheese and bread crumbs. Dip batons in the egg and roll in the bread crumbs. Fry batons until golden brown.