Preheat the oven to 220C/425F/Gas 7. Place the beetroot, ginger and garlic in a small baking dish. Cover with foil and bake until the beetroot is tender, about 1 hour. Cool slightly. Peel the beets, ginger and garlic and purée in a blender or food processor.
Heat 1 tablespoon of oil in a heavy large skillet over a medium heat. Add the shallot and thyme; sauté for 4 minutes. Add the chicken stock and wine; reduce for about 10 minutes. Add the stock-wine mixture to the beetroot mixture and purée until smooth, thinning with water, if necessary, to achieve a double cream consistency.
To serve, bring the beetroot sauce to a simmer in a saucepan, while stirring. Remove from the heat. Whisk in 4-5 knobs of butter and walnut oil to finish.