Combine the first six ingredients and mixed spices in a very large stockpot and cook until all the vegetables are very soft. Remove bay leaves and spice bag.
Cool soup slightly, and working in batches, purée the cooked mixture in a blender.
To remove seeds and skins, run each blended batch through a food mill.
Return the purée to the stockpot and add the margarine, ½ Creole seasoning mix, and brown sugar. Taste to adjust seasonings and add the rest of the Creole seasoning if you like.
In a small bowl, whisk together the flour and water to make a thin paste.
Add the paste slowly to the stockpot contents, stirring with the whisk as you do this. Bring the soup to a boil and cook until it thickens.
Ladle into jars leaving 1 inch of headspace.
Cap and seal. Place in canner with 2 to 3 inches of hot water.
Pressure cook for 1 hour and 25 minutes on High pressure. Once done, allow pressure to come down naturally before opening the cooker.