Start by heating the olive oil in a large pot or Dutch oven over medium heat. Once the oil is shimmering, toss in your sliced mixed mushrooms and diced yellow onions. Stir occasionally to ensure even cooking. Cook until the onions turn translucent and the mushrooms shrink in size, about 15 minutes.
Transfer the cooked mushrooms and onions to a bowl and set aside.
In the same pot, add unsalted butter and let it melt over medium heat. Whisk in the all-purpose flour along with sweet paprika, dill, salt, and pepper. Cook for about one minute while whisking constantly. Deglaze the pot by adding white grape juice vinegar, whisking until it evaporates.
Gradually whisk in your choice of low-sodium chicken broth or vegetable broth, adding it incrementally to allow the flour mixture to dissolve fully. Stir in the soy sauce along with the reserved mushroom mixture. Bring to a gentle simmer and let it cook until the liquid reduces by half, about five minutes.
Whisk in whole milk and sour cream into your simmering soup, bringing it back up to a simmer. Stir in your choice of vinegar just before taking it off the heat.
Off the heat, fold in freshly chopped parsley and give your soup a final seasoning with pepper to taste.