In a large saucepan, heat the oil and butter over medium heat. Add all the vegetables and cook for a few minutes, until they start to soften. Add the stock and cook for 20 minutes, until everything is very tender. Season with salt and pepper and stir in the cream.
Purée the soup in the pot using a hand-held immersion blender, or do it in batches in the blender or food processor until very smooth. Serve warm, or chill and serve cold.