I think each park has at least one CS restaurant that will serve breakfast.
In addition to the parks, every resort's CS restaurant has breakfast options. I'm not sure where you're staying, but I picked POP at random--here is a sample of their breakfast offerings:
Adult Breakfast Platter - scrambled eggs, potatoes, biscuit, sausage, and bacon $5.99
Ham and Cheese Omelet $6.49
Cheddar Cheese Omelet $6.49
Western Omelet $6.49
Breakfast Wrap $5.49
Breakfast Pizza $5.99
Vegetable Frittata $4.99
French Toast Platter with bacon or sausage $5.49
Pancakes with Topping with bacon or sausage $5.59
Pancake Platter with bacon or sausage $4.99
Chocolate Chip Pancakes with bacon or sausage $5.59
POP Waffle Platter w/bacon or sausage $5.49
Note that with breakfast, your CS will not include dessert, but will include juice (in addition to another beverage). Enjoy!