Soak the mushrooms in 1 cup of the water for 2 hours. Drain the mushrooms and strain the liquid through a coffee filter (this is to remove any sand).
In a large soup pot, bring the mushrooms, their soaking liquid, and the remaining water to a boil over high heat.
Add salt, then reduce the heat to low and simmer, covered, for 30 minutes.
Add the potatoes, increase the heat to medium low, and cook until the potatoes are tender, about 15 to 20 minutes.
Remove from the heat. With a slotted spoon, remove the mushrooms. When they are cool enough to handle, chop them very fine.
Using the slotted spoon, transfer the potatoes to a food processor. Add 1 cup of the cooking liquid and process until pureed.
Whisk the potatoes back into the cooking liquid in the pot. You will have to stir them thoroughly with a fork or wire whisk until there are no lumps. Set aside.
In a small skillet, sauté the bacon until it renders its fat. Drain off all but 1 Tablespoon of the fat, then add the onion and the mushrooms. Saute, stirring occasionally, over medium high heat until the mixture is well browned, about 15 minutes.
Return the soup to low heat. Add the cream and simmer gently for 2 minutes, until the soup is about to boil.
Stir in the sautéed onion, mushroom, and bacon mixture. Season with a few dashes of paprika and salt and pepper, then simmer for another 3 to 4 minutes. Serve garnished with fresh dill. Serves 6.