In a large pot, heat the olive oil over medium heat. Add the chopped onion and sauté until translucent, about 5 minutes.
Add the minced garlic and sliced mushrooms to the pot. Cook for another 5-7 minutes, stirring occasionally, until the mushrooms are tender.
Stir in the dried thyme and paprika, cooking for an additional minute to release the flavors.
Sprinkle the flour over the mushroom mixture and stir well to combine. Cook for 1-2 minutes.
Gradually pour in the vegetable broth while stirring to avoid lumps. Bring the mixture to a boil, then reduce the heat and let it simmer for 15 minutes.
Stir in the milk and soy sauce, then season with salt and pepper to taste. Simmer for another 5 minutes.
Remove from heat and garnish with fresh parsley before serving.