Heat oil in a large saucepan over medium heat. Add carrot, onion and garlic; cook, stirring, until the onion is soft, 3 to 4 minutes. Stir in broth, chickpeas, corn, peas, salt and pepper. Bring to a boil over high heat. Reduce heat to maintain a simmer and cook, stirring occasionally, for 10 minutes. Stir in spinach and cook until wilted, about 1 minute. Serve the soup topped with cilantro, if desired.