Melt the butter (4 tablespoons) in a medium or large pot over medium high heat. Once it's melted, continue heating until foamy and beginning to turn brown.
Immediately add the diced onion and mushrooms. Season with salt and pepper. Stir, turn heat down to medium, then allow to sauté untouched for approximately 5 minutes, or until liquid has mostly evaporated.
Add flour (1/4 cup); stir to coat.
Add chicken broth (4 cups), stir, bring to a boil.
Turn heat down to simmer. Add cubed brie (8 oz.) and continue simmering until melted (if there are a few chunks that won't melt, don't worry about it).
Use an immersion blender to puree the soup to desired consistency (alternatively, you can use a standard blender in batches).
Add the heavy cream (1 cup) to soup and stir in. Turn off heat, and taste and adjust seasonings if necessary.
Serve hot, garnished with croutons and/or parsley, if desired.
Don't worry about removing every speck of rind from the brie- it won't melt into the soup but since you are pureeing it anyway, a little bit here and there won't matter.
For a lower fat version, reduce butter to two tablespoons and use whole milk or half and half instead of heavy cream.
For a gluten free version, substitute cornstarch for the flour (or omit the flour).
For a more intense mushroom flavor, add some dried porcini mushrooms.
Freeze the leftovers or an extra batch in an airtight container for up to 6 months.
The provided nutrition information does not include any added sodium from seasoning to taste, any optional ingredients, and it does not take brands into account. Feel free to calculate it yourself using this calculator or by adding the recipe to Yummly.