Using a large pot, melt the butter over medium-high heat. Add the onions, celery, and cayenne. Cook, stirring, until soft.
Add the garlic and cook for less than a minute before adding the mushrooms, thyme, salt and pepper.
Cook, stirring, until the mushrooms give off their liquid and start to brown. This should requireabout 7 minutes.
Add the brandy and bring it to a boil. Cook until the mushrooms are glazed, which should take about 2 minutes.
Add the stock and return everything to a boil. As soon as it boils, immediately turn it down to medium low and continue to simmer uncovered for about 15 minutes.
Remove the soup from the heat and puree it with a hand held immersion blender, or you can use a food processor.
Place the soup back on the heat, add the cream, and return to a simmer. Adjust the seasoning and serve.