Heat oil in the bottom of a 4- or 6-quart slow cooker on High. Add zucchini, onion, carrot, celery, garlic, salt, and pepper; stir to combine.
Pour in vegetable stock, chickpeas, undrained tomatoes, and green beans. Cover and cook on Low for 6 to 7 hours.
Add ditalini and cook for 1 more hour. Stir in pesto and serve.
