In a large saucepan, melt the butter over medium heat. Add the diced onion and sauté for about 4-5 minutes until it softens and becomes translucent.
Stir in the sliced mushrooms and cook for about 8-10 minutes, allowing them to brown and their moisture to evaporate, stirring occasionally.
Sprinkle the flour and paprika over the mushrooms, stirring to evenly coat and cook for an additional 2 minutes to eliminate the raw flour flavor.
Gradually pour in the vegetable broth while continuously stirring to avoid lumps. Add the heavy cream and soy sauce, mixing until fully incorporated. Bring to a gentle simmer and cook for 12-15 minutes, stirring occasionally.
Remove the pot from heat. Fold in the Greek yogurt, apple cider vinegar, fresh chives, thyme, and add salt and pepper to taste. Allow the soup to rest for a few minutes to meld the flavors.