Bring water, milk, salt and cinnamon to a boil and add oats. Cook according to package directions, or until oatmeal reaches desired consistency.
Meanwhile, process ½ cup hominy in a food process until roughly chopped. Reserve.
Take oatmeal off of heat and stir in sweetener and processed hominy. To finish, ladle into bowls, top with remaining hominy, a pat of butter and more sweetener if desired.