Heat the vegetable stock in a saucepan and add the chopped tomatoes. Bring to the boil, then turn the heat down and add the carrots. Let the soup gently simmer, until the carrots are cooked, for approximately 15 minutes.
Stir in the beans and spinach. Heat until the spinach has wilted, stirring occasionally. Add the pesto and black pepper. Heat for a minute longer and then serve.