In a large pot or Dutch oven, heat the olive oil over medium heat. Add the chopped onion and sauté for about 5 minutes, until translucent.
Add the minced garlic and sliced mushrooms to the pot. Cook for about 10 minutes until the mushrooms are tender and have released their moisture.
Stir in the Hungarian paprika, dried thyme, salt, and black pepper. Cook for another 2 minutes to allow the spices to bloom.
Pour in the vegetable broth, and bring the mixture to a simmer. Let it cook for about 10 minutes.
After simmering, remove the pot from heat. You can blend the soup for a smoother texture using a blender or an immersion blender, if desired. Otherwise, leave it chunky.
Return the pot to low heat and stir in the milk, soy sauce, and lemon juice. Let it heat through for about 5 minutes without boiling.
Taste and adjust seasoning as needed. Serve the soup hot, garnished with a dollop of sour cream and a sprinkle of fresh parsley, if using.