In an electric blender or food processor, purée the chickpeas, red peppers, lemon juice, tahini, garlic, cumin, cayenne and salt. Process, using long pulses, until the mixture is fairly smooth, and slightly fluffy. Make sure to scrape the mixture off the sides of the food processor or blender in between pulses.
Transfer to a serving bowl and refrigerate for at least 1 hour. (The houmous can be made up to 3 days ahead and refrigerated. Return to room temperature before serving.) Sprinkle the hummus with the chopped parsley before serving. Drizzle with olive oil if desired.