Heat oil in a large pot or Dutch oven over medium. Add mushrooms and onions and cook, stirring occasionally, until onions are translucent and mushrooms have shrunk in size by half, 15 minutes.
Transfer onions and mushrooms to a bowl.
Add butter to now empty pot and let melt over medium heat. Whisk in flour, paprika, dill, salt, and pepper and cook, whisking constantly, 1 minute. Deglaze pan with wine, whisking, until evaporated.
Whisk broth in by increments, allowing flour mixture to adequately dissolve into broth before adding more. Stir in soy sauce and reserved mushroom mixture. Bring soup to a simmer and cook until liquid has reduced by half, about 5 minutes.
Whisk in milk and sour cream, bring soup back to a simmer then stir in vinegar. Off heat, add parsley and season with pepper to taste.