Place the dried mushrooms in a large bowl. Bring the broth to a boil and pour over the dried mushrooms. Set aside to rehydrate for about 20 minutes.

Using a slotted spoon, remove the mushrooms and reserve the broth. Roughly chop the mushrooms.

Heat the butter in a large pot over medium-high heat. Add the button and rehydrated mushrooms and cook, stirring occasionally, until soft and somewhat dry, about 6 minutes. Add the leek and shallot and cook, covered, stirring occasionally, until translucent, about 4 minutes. Stir in the flour and cook, stirring, for 2 minutes more.

Pour in the reserved mushroom broth, taking care not to add any grit or dirt that may have fallen to the bottom of the boil, and bring to a boil while whisking constantly. Tie the parsley sprigs, fresh thyme, and bay leaf together with a piece of kitchen twine and add to the soup. Lower the heat and simmer for 10 minutes. Remove from the heat and allow to cool.

Remove and discard the herb bundle. Working in batches, transfer the mixture to a blender and puree until smooth. Using a sieve over a large bowl, strain the mushroom puree. Return the puree to the pot and reheat over medium heat.

Whisk the heavy cream, Madeira, and salt into the soup and season with pepper to taste. Divide among warm soup bowls and serve immediately.