Step 1Soak dried mushrooms in hot water 20 minutes, then drain liquid through paper towels (to catch any grit) and reserve. Set liquid and mushrooms aside.
Step 2Heat butter in 3-quart pot over medium-high heat. When hot, add onions. Cook, stirring often, until softened, about 5 minutes. Add white and shiitake mushrooms and garlic. Cook, stirring often, until heated through, about 5 minutes. Add reserved liquid and 1 1/2 cans broth. Bring to boil, then reduce heat and simmer, covered, 30 minutes. Let cool at room temperature.
Step 3Strain vegetables from liquid, reserving both. Puree vegetables in blender with 1/4 cup chives. Add some liquid and puree until mixture is very smooth, about 1 to 2 minutes.
Step 4Return to pot. Stir in cream, and if soup is too thick, add remaining broth (and water if needed). (Can be made ahead up to this point and refrigerated 2 days or frozen up to 1 month. To serve, gently reheat until hot; do not boil. Add water if soup is too thick.) Taste; adjust seasoning. Serve hot, garnished with snipped chives.