Combine lemon juice and water in small bowl or measuring cup. Whisk together tahini and 2 tablespoons oil in second small bowl or measuring cup.
Process chickpeas, artichokes, garlic, salt, cayenne, and lemon zest in food processor until almost fully ground, about 15 seconds. Scrape down bowl with rubber spatula.
With machine running, add lemon juice-water mixture in steady stream through feed tube.
Scrape down bowl and continue to process for 1 minute.
With machine running, add oil-tahini mixture in steady stream through feed tube; continue to process until hummus is smooth and creamy, about 15 seconds, scraping down bowl as needed.
Transfer hummus to serving bowl. Sprinkle reserved artichokes and parsely or mint over surface, cover with plastic wrap, and let stand until flavors meld, at least 30 minutes.
Drizzle with olive oil. Sprinkle with minced herbs and cayenne pepper and serve with toasted pita chips.