Peel and thickly slice the jerusalem artichokes, parsnips and onion and place on a large baking tray. Add the garlic cloves (leaving them in their skin), and scatter over the thyme (stripping the leaves off the main stalks).
Drizzle over the oil, season well with salt and black pepper, then mix well then roast in the oven for 20 minutes.
Squeeze the garlic flesh out of the skins, (discard the skins), and remove any remaining thyme stalks, then tip the roasted vegetables into a saucepan.
Pour in the dairy-free milk and vegetable stock.
Bring to the boil and simmer for 5 minutes, then blitz to a smooth purée in a blender, food processor or with a hand blender.
Taste and adjust seasoning as required. Serve scattered with walnut pieces and chopped parsley.