In a large stock pot combine peanuts in shells, 3 1/2 cups vegetable stock, beer, cola, and thyme. Cook's Note: Liquid should cover the peanuts.
Bring the mixture to a boil, reduce the heat and simmer, about 5 to 6 hours, adding additional vegetable stock as needed to ensure there is enough liquid to cover the peanuts at all times. Cook's Note: Peanuts are done when you can easily crush a shelled peanut when placed between your index finger and thumb.
Once the peanuts are cooked, remove them from the heat and strain the liquid into a separate container, reserving 1/2 cup cooking liquid. Allow the peanuts to cool enough to handle. Shell all peanuts. Put the peanuts in a food processor and pulse them while slowly adding the 1/2 cup reserved cooking liquid. Do not puree. The texture should be like fork-mashed potatoes. Season the peanut mash with salt and pepper, to taste.