Whisk the tahini and olive oil together in a small bowl or measuring cup; set aside.
Process the chickpeas, red peppers, garlic, salt and cayenne in a food processor until almost completely ground, about 15 seconds, scraping down the sides of the bowl as needed. With the machine running, add the lemon juice and process for 1 minute. Scrape down the sides of the bowl, then begin processing again and with the machine running, add the tahini mixture and continue processing until the hummus is smooth and creamy, scraping the bowl as necessary, about 15 seconds.
The hummus can be stored in an airtight container (or in a bowl covered with plastic wrap) in the refrigerator for up to 3 days. Garnish with parsley before serving.