Heat the oil in a sauté pan and gently cook the onion until translucent, about 5 minutes. Add the green beans, potato and carrot dice. Pour over 4 cups/1-litre vegetable water or stock. Season with salt and pepper, add the bay leaf and the thyme. Bring to a boil, and simmer 10 minutes.
Add the kidney beans and the zucchini and continue cooking until all the vegetables are tender, about 10 minutes longer. Stir through the tomato.
Ladle the soup into bowls. (Remove the bay leaf and thyme sprigs). Add a spoonful of pesto to each bowl, and grate over Parmesan cheese.