Pour the rinsed chickpeas into a medium microwave-safe bowl. Heat until hot, about 60-90 seconds. Stir in the olive oil, lemon juice, salt, pepper, and cayenne. Let sit at room temperature for about 30 minutes, to allow the dressing to absorb into the chickpeas.
Add the shredded carrots, olives, and parsley to the chickpea mixture. At this point, you can cover and place in the fridge for a few hours, or serve it immediately.
Split the arugula or mixed greens between two (to serve as an entree) or 4 small (to serve as a side) bowls. Top each bowl with equal amounts of the chickpea mixture. Garnish with additional parsley if desired. (Note that it's important to keep the arugula separate from the chickpea mixture until you're ready to serve it, or the arugula will wilt).