Rinse the mushrooms to remove any dirt and pat dry with paper towels. Chop the mushrooms and, if desired, slice a few to use for garnish.
In a large stockpot or dutch oven, heat 1 tablespoon of olive oil over medium-high heat. Add the onions and garlic and cook gently for about 3 minutes.
Add the mushrooms, thyme, salt, and pepper. Cook, stirring regularly, until the mushrooms start to brown, about 5 minutes. Spoon out 3 tablespoons of mushrooms and keep them for later (if using for garnish).
Stir in the second tablespoon of oil, add the flour, and cook, stirring constantly for about 30 seconds to a minute until the flour and liquid forms a thick paste.
Add the vegetable broth and bring the mixture to a simmer. Stir to dissolve any remaining flour. Once simmering, reduce the heat to medium-low and add the milk.
Simmer uncovered, stirring occasionally, for about 15-20 minutes.
Transfer to a blender and blend to a creamy consistency. Once blended, return to the pot.
Add the soy sauce and cook for a further minute. Taste and adjust seasoning, as necessary.
Spoon the soup into bowls, garnish with the remaining mushrooms, if desired, and serve.