Preheat the oven to 300°. Bake the bread slices on a baking sheet for about 1 hour and 40 minutes, until deeply browned.
In a pot, melt the butter. Add the mushrooms and the garlic; season with salt and pepper. Cover and cook over moderate heat, until the mushrooms are softened, 5 minutes. Add the broth and 1/2 cup of the cream; bring to a boil. Cover and simmer until the mushrooms are tender, 10 minutes.
Add the toasted bread to the soup; simmer until softened, 5 minutes. Working in batches, puree the soup in a food processor. Return the soup to the pot, season with salt and pepper and keep warm.
In a saucepan, bring the remaining 1/4 cup of cream to a boil. Remove from the heat; whisk until frothy. Ladle the soup into bowls, top with the frothed cream, garnish with the dill and portobello gills and serve.