Melt butter in a heavy saucepan. Add the onions, shallots, garlic, Shiitake stems, white mushrooms, and saute for about one hour.
Add the brandy and let boil for 30 seconds then add half the water and bring to a simmer.
Add the heavy cream slowly, stirring it in. The total temperature should not be reduced much. Simmer for about 20 minutes, adjust consistency.
Strain, season, and add Shiitake mushrooms. Season again and serve.