Heat the olive oil in a large soup pot. Add the leeks carrots, and garlic tossing to coat them with the oil. Add a pinch of salt and cover the pot. Allow the vegetables to sweat for 5 - 7 minutes.
Add the Ham Broth and the thyme leaves to the pot. Cover and bring to a boil. Reduce the heat to low and simmer covered for 20 - 30 minutes, stirring occasionally.
At this point you can remove the thyme sprigs as the leaves have probably fallen off and the sprigs have done their flavor magic. Add the sweet potatoes and corn and simmer 20 minutes more or until the sweet potatoes are tender.
While the soup is simmering, blanch the snow peas and haricot vert. Put them in boiling water briefly, then remove them to a bowl of ice water. When they are cold drain them well. This will leave them tender crisp and bright green. Set them aside.
When the soup is done, taste it and add salt and pepper as needed. Place a few haricot vert and snow peas into each soup bowl. Ladle the soup into the bowls and serve.