Combine tahini and fresh lemon juice in a food processor. Process for 1 minute until whipped and smooth.
Add the minced garlic, extra virgin olive oil, cumin, and salt to the whipped tahini. Process for another 30 seconds.
Drain and rinse the chickpeas. Add half of the chickpeas to the food processor and blend for 1 minute. Scrape the bowl, add the remaining chickpeas, and blend until thick and quite smooth.
With the food processor running, slowly add ice water, one tablespoon at a time, until the mixture reaches your desired ultra-creamy consistency.
Transfer to a serving bowl. Drizzle generously with additional olive oil, and sprinkle with paprika, sumac, and chopped fresh parsley. Serve immediately with warm pita bread or toasted bread.