Melt the butter in a large pot over medium heat. Add the onions and mushrooms and sauté for 7-8 minutes or until the onions are softened and the mushroom liquid has completely evaporated.
Add the garlic and sauté for 1 minute until fragrant.
Add the flour and cook, stirring constantly, for 2-3 minutes, or until golden and nutty, scraping up any browned bits from the bottom of the pot as needed.
Stir in the chicken broth, bouillon paste, salt, pepper, and dried thyme. Increase the heat to medium-high and bring to a boil. Reduce the heat to medium-low and simmer the soup with the lid ajar for 10 minutes. Stir the soup occasionally to prevent the mushrooms from sticking to the bottom of the pot.
Add the brie and milk and cook for 2-3 minutes or until the cheese is melted (it’s okay if a few chunks of cheese remain).
Very carefully transfer half the soup to a blender. Add the lid, remove the vent, and cover the hole with a clean dish towel. Blend until your desired consistency. Transfer the soup to a clean bowl, blend the remaining portion, and transfer all the blended soup back to the soup pot.
Return the blended soup to the pot, and heat over low for 2-3 minutes until hot.
Remove the soup from the heat, slowly drizzle in the red wine vinegar (if using), stir well, and season to taste with salt and pepper. Enjoy hot, garnished with parsley and/or croutons if desired.