Melt the butter in a large pan over medium heat until foamy. Add the onions, sunchokes and potatoes. Cover and cook over low heat for 10 minutes.
Uncover and cook, stirring often so they don't stick, for and additional 8 minutes, or until vegetables are soft.
Stir in the flour and half of the brandy, and cook for 1 minute. Gradually stir in about 2 cups of the stock, stirring continuously, until the soup thickens and reaches a boil. Turn down heat and simmer for an additional 5 minutes.
Transfer to a food processor and puree until smooth, adding more stock to desired consistency, possibly up to a cup. Return to the pan, add the half and half and season well with salt and freshly ground black pepper, then reheat. Finish with another tablespoon of brandy stirred in (optional, but worth it). Sprinkle with the chopped parsley for serving, if desired.
Delicious served with a nice warm whole wheat baguette!