Preheat the oven to 220 C / Gas 7. Line a rimmed baking tray with greaseproof paper.
Spread potatoes, parsnips, onions and garlic on the prepared baking tray. Drizzle olive oil on top. Season with paprika, salt and pepper. Toss until evenly coated and spread back out into an even layer.
Roast in the preheated oven until browned in spots, about 40 minutes.
Transfer roasted vegetables into a large pot. Cover with vegetable stock. Bring up to a simmer; cook until vegetables are very soft, about 30 minutes. Remove from heat.
Puree hot soup carefully with an immersion blender until smooth. Stir in cream until thoroughly incorporated. Season with salt.
Ladle soup into bowls. Garnish each bowl with dollops of creme fraiche, bacon and chives.