In a heavy 4-quart pot over mediumlow heat, warm the butter and oil. Add the onion, fennel, and parsnip. Cook, stirring frequently, to soften the vegetables without browning, about 7 minutes. Add the cauliflower, turnips, 3-1/2 teaspoons salt, broth, and sugar. Bring to a boil over high heat, then lower the heat, cover, and simmer until the vegetables are soft, 25 minutes. Turn off the heat and let sit, covered, for a few minutes.

Transfer the soup in batches to a blender, cover tightly, and carefully puree until smooth and silky, about 2 minutes. Transfer to a clean pot. Season to taste with salt. If the soup seems too thick, add a few tablespoons of water. To serve, reheat, ladle into warm soup bowls, and garnish with a few bits of gold leaf and a small dollop of caviar.