Soak mushrooms in 3/4 cup water until tender, 20 to 30 minutes. Set aside.
Melt half the butter and saute the onions, meats, and rehydrated mushrooms. Add the stock and liquid from the mushrooms and bring to a boil. Make a bouquet garni by tying the bay leaves and peppercorns tightly in cheesecloth. Lower the heat and add the bouquet garni, pickles, capers, and marinated mushrooms. Simmer 10-15 minutes.
Melt remaining butter in a skillet and cook the tomatoes and tomato paste for a few minutes, then add the flour and saute for another few minutes. Add a cup of the soup to the skillet and stir in well, then return pan ingredients to the soup pot.
Add the olives, dill, marjoram, garlic, pickle juice, and paprika. Adjust soup's seasoning with salt and pepper; simmer another 10-15 minutes.
Remove pot from heat and remove bouquet garni. Adjust seasonings and serve with sour cream.