Melt the butter in a large pot over medium heat until foamy. Add the onions, Jerusalem artichokes and potatoes and cook, covered, over low heat for 10 minutes. Uncover and cook for and additional 8 minutes.
Stir in the brandy and flour and cook for 1 minute. Gradually stir in about 3/4 of the stock, stirring continuously, until the soup boils and thickens. Simmer for a further 5 minutes. Transfer to a food processor or blender and purée until smooth, adding more stock if needed.
Return to the pot, stir in the cream and season well with salt and freshly ground black pepper. Simmer until heated through, but do not boil. Sprinkle with chopped parsley to serve.