Heat the oil in a large saucepan over medium heat. Add the onion and cook, stirring, for 3 mins or until the onion softens. Add the garlic and fennel and cook, stirring occasionally, for 5 mins or until the fennel begins to caramelise. Add the celeriac and parsnip and stir until well combined. Pour over 8 cups (2L) of water.
Use kitchen string to tie the parsley stalks into a bunch and add to the pan. Bring the mixture to the boil. Reduce heat to low and simmer, stirring occasionally, for 45 mins or until the parsnip and celeriac are tender. Set the soup aside to cool slightly.
Meanwhile, place the parsley leaves, dill sprigs, oil and salt in a small food processor and process until the mixture is finely chopped and bright green.
Remove and discard the parsley stalks from the soup. Transfer half the soup to a blender and blend until smooth. Transfer the soup to a clean saucepan. Repeat with the remaining soup. Add half the sour cream and stir to combine. Place over low heat and cook, stirring, for 5 mins or until heated through. Taste and season with salt and pepper.
Divide the soup among serving bowls. Top with a dollop of the remaining sour cream. Drizzle with the parsley and dill mixture. Top with reserved fennel fronds and serve with freshly ground black pepper.