Method:
Steam carrots until they are very tender, about 10 minutes. Transfer carrots to the bowl of a food processor. Set aside to cool.
Steam green beans until bright green and crisp-tender, 4 to 5 minutes. Immediately cool beans in cold water. Drain and pat dry.
When carrots are cool, add sour cream, mayonnaise, shallot, salt and cayenne to the food processor and process until smooth. Add dill and pulse until combined. Transfer dip to a bowl and serve with green beans for dipping.