Preheat oven to 400 degrees.
Peel and slice zucchini. Put in a saucepan together with water and chicken base. Cover and boil until 3/4 of the moisture has evaporated about 20 minutes.
Using a wooden spoon, break zucchini into small pieces. Gradually stir in corn meal then add milk or cream.
Stir over medium heat until mixture is medium thick. Add more cornmeal if necessary. Transfer to a baking dish.
Sprinkle with grated cheese. Bake for 15 to 20 minutes, or is golden brown