Warm butter and olive oil in a large stock pot over medium heat. Add carrots, celery, onion, celery root and garlic, stirring to coat in the butter/oil. Sauté the vegetables, stirring occasionally, until golden brown, about 10 minutes.
Wrap bay leaves and thyme sprigs within the parsley bunches then secure the entire bundle with a string (see picture above). Add the bundle to the pot with peppercorns and prunes. Add enough cold water to cover everything (about 16 cups).
Bring mixture to a gentle boil. As soon as the boil begins, drop heat to very low and simmer for 1 1/2 hours. The stock should not bubble away during this time period. It should remain fairly still with just a few bubbles coming to the top occasionally. Do not stir. Stirring will cause the vegetables to break down and cloud your stock.
Double strain the mixture into a large bowl. Start with a medium mesh strainer to remove all of the large particles then strain again with a fine mesh strainer to remove any tiny bits. Strained vegetables can be saved for later consumption (but will need some salt!).
To chill rapidly, place the bowl in a sink filled with ice and water. Gently stir until the stock chills. Cover and store in the refrigerator for up to 1 week or in the freezer for 6 months. I like to measure out 2 cups worth of the stock into small ziplock bags. I then freeze these bags for future use.