In a large saucepan, combine the peas, lima beans, bay leaf, 2 sprigs of thyme, stock, whole carrot, whole celery stalk, onion halves and garlic head. Place the saucepan over medium heat and bring to a simmer. (Do not season beans now; you never season beans at the beginning of cooking because that makes them tough).

While the beans are simmering, with a large ladle or spoon, skim off the scum on the surface. Cook the peas and beans until just tender, about 20 minutes. Once the beans are cooked, remove the herbs, carrot, celery, onion and garlic from the pan and discard.

To finish the dish, add the diced carrot, diced celery, diced onion, salt, pepper and butter to the saucepan. Return the stock with the beans and peas to a simmer over the medium heat and cook until the liquid is glossy and emulsified, about 20 minutes.

Remove the leaves from the remaining 2 sprigs of thyme. Garnish with the thyme leaves for fragrance and serve.

Note: When skimming the scum off any cooking liquid it is easier if your wrap your spoon in cheesecloth rinse it and repeat.