Step 1Soak the dried mushrooms in 1 cup of hot water for 15 minutes. Drain, reserving the liquid.
Step 2Heat 1 tablespoon of the butter in a heavy pot over medium-high heat. Cook the onion until softened, about 4 minutes. Stir in the sliced mushrooms; cook until they exude moisture, about 6 minutes. Stir in the dried mushrooms. Measure the reserved mushroom liquid with water to make 4 1/2 cups. Add to the pot. Add the salt and pepper. Bring to a boil, reduce the heat and simmer, half-covered, for 30 minutes.
Step 3Cook the potato in simmering water until soft, about 15 minutes; reserve 1 cup of the cooking liquid. Mash the potato until smooth; stir in the liquid.
Step 4Heat the remaining 2 tablespoons of butter in a small nonstick pan over medium heat until light brown; stir in the flour. Cook 4 minutes. Stir in the garlic; cook until the garlic just starts to brown, about 3 minutes. Remove from the heat. Stir in the reserved potato mixture.
Step 5Stir the mushrooms into the flour mixture. Simmer until thickened, about 10 minutes. Drizzle 1/2 cup of the hot soup into the sour cream mixture, stirring constantly. Slowly stir back into the soup. Add the parsley and dill. If the soup is too thick, add more water.