Place Green Cabbage (12 cup) in a large bowl. Bring enough water to a boil — I fill a tea kettle, but you could always fill a large sauce pan — to submerge the cabbage in the bowl. Pour the water over the cabbage; let sit one minute or longer; drain.
Meanwhile, in a large pot, heat the Olive Oil (1/4 cup) over high heat until it shimmers. Add the Onion (2 cup) immediately turn the heat down to medium or low, and cook, stirring, until they are soft, about 15 minutes.
Sprinkle with All-Purpose Flour (1/2 cup) and stir. Add the Water (10 cup) stirring rapidly with a wire whisk.
When the mixture simmers, add the cabbage, Carrot (2 cup), Potato (2 cup), Kosher Salt (2 teaspoon), Freshly Ground Black Pepper (to taste), Caraway Seeds (2 teaspoon), White Balsamic Vinegar (1/4 cup) and Granulated Sugar (1 teaspoon). Simmer, stirring every so often, for about about 30 minutes.
Stir in the Heavy Cream (1 cup) and simmer 5 minutes. Add the Fresh Dill (1/4 cup) to the pot. Taste and adjust as needed with more salt and pepper to taste.
Serve, adding more chopped dill to each bowl if desired.