Aunt Jojo's Politically Incorrect Potato and Sausage Soup

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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