Heat 5 tablespoons of olive oil in a large heavy pot over medium heat. Add the rough chopped leeks and garlic cloves and cook until soft, about 7 minutes. Add the carrots and potatoes and cover and cook for about 10 more minutes. Add the stock, bay leaves, thyme, and salt and allow to simmer for 20 minutes. Check to make sure the vegetables are soft.
Blend the soup in a blender until the vegetables are puree. Serve with a swizzle of olive oil and fresh or dried herbs like chives, basil, parsley or thyme.