In a bowl, combine cornmeal, 1 cup cold water and salt. Stir well.
Bring remaining 3 cups water to a rolling boil. Stir in the cornmeal mixture and bring back to the boil, stirring constantly. Reduce to a simmer and stir in cheese.
Simmer 20 minutes, stirring often, until very thick. Pour into loaf pan and refrigerate until set, about 4 hours.
Turn out of loaf pan and slice lengthwise, 1/2" thick. Cut each slice into fingers about 1" wide. Fry fingers in olive oil until golden brown on both sides, and hot all the way through. Serve with tomato sauce on the side.