Bread thickens this soup and enhances its texture.
Heat oven to 425 degrees. Wrap two heads garlic in foil, and roast until soft and golden, about 1 hour; set aside.
Meanwhile, melt butter in small stockpot over medium heat. Add carrots, celery, parsley, 1 teaspoon salt, 1/4 teaspoon pepper, and raw cloves from one head of garlic, peeled. Squeeze out cloves from one roasted head of garlic. Add all but four cloves to pot, reserving these for later use. Cook, stirring often, until vegetables are soft, about 15 minutes. Add stock; bring to a boil. Reduce heat, and simmer until stock is very flavorful, about 30 minutes. Strain soup, pressing down on solids. Discard solids; return soup to pot.
Slice remaining three garlic heads down the center; add to stock. Simmer until cloves are soft, about 20 minutes. Remove garlic; separate cloves (cloves will easily push out from heads after being cooked), and discard heads. Blend stock, garlic cloves, and white bread in food processor until smooth. Return soup to pot; simmer. Add cream and sherry, and adjust seasoning with salt and pepper.
Spread reserved roasted garlic on sliced baguette; sprinkle with grated cheese. Toast on baking sheet in a 450 degree oven until golden and melted, about 6 minutes.
Place one crouton in each bowl; ladle soup over bread. Sprinkle with nutmeg.
Homemade chicken stock can be replaced with low-sodium canned chicken stock.