In a medium bowl, combine the dried mushrooms and 2 cups of the warm water. Cover with plastic and let soak overnight.
The next day, remove the mushrooms from the soaking liquid without disturbing the sediment at the bottom and chop them into smaller pieces.
Carefully add the soaking liquid into a large pot without disturbing the sediment at the bottom. Add the chopped mushrooms, 4 cups water, the whole onion, sauerkraut, and salt and pepper to taste.
Bring to a boil, reduce heat and simmer 1 1/2 to 2 hours or until mushrooms are tender.
Remove onion and add 3/4 cup sauerkraut juice.
In a small skillet, brown the flour in 4 tablespoons oil to make a dark brown roux and add to soup, whisking until smooth.
Temper the mixture of 1/2 cup flour and 1 cup water by adding a little hot soup into it, whisking until smooth. Pour the tempered mixture through a strainer back into the hot soup, stirring constantly.
In a large skillet, add 1 to 2 tablespoons canola oil and brown the sliced onion until darkand caramelized. Set aside.
When ready to serve, add browned onions to soup, mixing well.