In a large pot, melt the butter over medium-high heat. Add the onions, celery, and cayenne and cook, stirring, until soft, about 4 minutes. Add the garlic and cook for 30 seconds. Add the mushrooms, thyme, salt, and pepper, and cook, stirring, the mushrooms give off their liquid and start to brown, about 7 minutes. Add the brandy, bring to a boil and cook until glazed, about 2 minutes. Add the stock and return to a boil. Reduce the heat to medium-low and simmer uncovered, stirring occasionally, for 15 minutes.
Remove from the heat and puree with a hand-held immersion blender, or in batches in a food processor. Add the cream, return to a simmer, and cook for 5 minutes. Remove from the heat and adjust seasoning, to taste.
Preheat the oven to 400 degrees F.
Rub both sides of the French bread slices with the crushed garlic and place on a baking sheet. With a pastry brush, brush 1 side with the olive oil. Top with a fine sprinkling of the cheese and bake until the cheese is bubbly, about 5 minutes. Remove from the oven.
To serve, ladle the soup into bowls and top each serving with 2 croutons.
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