Add potatoes, onions, celery, salt, pepper, savory and 8 cups water to a large pot on high heat. Boil until the potatoes are tender, about 20 minutes. Remove from heat and let cool a few minutes.

Stir in heavy cream and buttermilk. Return pot to stove on medium low heat.

Make a cornstarch slurry with cornstarch and 3 tbsp water by whisking together. Add to soup and whisk to combine. Heat, whisking often, until soup reaches desired thickness. Garnish with fresh parsley, if desired. Serve hot.