Rinse the dried beans well to remove any debris.
Heat the olive oil over low-medium heat in a large Dutch oven until it shimmers. Next, add the garlic, celery, and shallots to the oven and cook the mixture until it’s just lightly browned. Once the mixture is lightly browned, season with the black pepper.
Next, add the cannellini beans, bay leaves, broth, 2 cups of water, and salt. Increase the oven's heat to high. Bring beans to a boil and cook for 10 minutes. After 10 minutes, reduce the heat to low. Simmer the beans, partially covered, for 90 minutes. The beans should be tender but not mushy.
Add the remaining 8 cups of water, lima beans, and Better Than Bouillon Vegetarian No Chicken Base paste, and stir gently. Cover the beans and increase the oven’s heat to high. Bring all the ingredients to a boil and cook for an additional 10 minutes. Reduce the heat to low. Add the thyme sprigs. Simmer, partially covered, for 2 hours. The beans are done when they are creamy and translucent. If after 2 hours your beans are still too firm, continue to simmer them, partially covered, for another 20 to 30 minutes. Be sure to check the beans for doneness every 5 minutes or so. The total cooking time, with unsoaked Rancho Gordo beans, is approximately 3½ hours.
Remove the bay leaves and thyme stems and discard.