In a large stockpot, combine the onion, garlic, celery, carrots, parsley, parsnip, peppercorns, bay leaves, and thyme with 4 qt/3.8 L water. Cover and bring to a boil over high heat. Reduce the heat to medium-low and simmer for 1 hour, stirring occasionally. Uncover the pot and simmer for another 20 minutes to slightly reduce the stock to intensify the flavor. Remove from the heat and let cool for at least a half hour before straining. The stock can be refrigerated, covered, for up to 1 week and frozen for up to 1 year.