Peel the parsnips and carrots and cut into approximately 2 inch pieces. Fill a large saucepan with 6 cups cold water and bring to boil and add salt. Add carrots, garlic and 4 sprigs of thyme in the water, reduce heat and simmer for about 5 minutes. Add the parsnips and continue cooking until both the carrots and parsnips are soft, about 15 minutes.
Remove the parsnips & carrots from the heat, drain and discard the thyme sprigs. Transfer the carrots, parsnips and garlic to the work bowl or a food processor. Add butter, cream and 1 tablespoon thyme leaves and process until completely smooth. (Placing in a large mixing bowl and mixing with a hand mixer can also puree the vegetables). Season to taste with salt and pepper, garnish with fresh thyme and serve immediately. If the puree is made in advance of serving, reheat in a saucepan over low heat and serve.