6 to 8 Yukon gold potatoes (or 4 large baking potatoes, like russets), peeled and diced into 1-inch pieces
4 cups chicken stock
2 pounds hot sausage, out of the casing
1 1/2 cups diced onion
1 3/4 cups finely diced celery
4 ounces butter
1 quart heavy whipping cream
3 or 4 tablespoons balsamic vinegar (white or dark)
1 tablespoon vanilla
4 tablespoons finely chopped flat-leaf parsley
Salt and pepper, to taste